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Academic literature on the topic 'Binomial ideals'

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Published: 11 March 2023

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Journal articles on the topic "Binomial ideals"

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Eisenbud, David, and Bernd Sturmfels. "Binomial ideals." Duke Mathematical Journal 84, no. 1 (July 1996): 1–45. http://dx.doi.org/10.1215/s0012-7094-96-08401-x.

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MartÍnez de Castilla, Ignacio Ojeda, and Ramón Peidra Sánchez. "Cellular Binomial Ideals. Primary Decomposition of Binomial Ideals." Journal of Symbolic Computation 30, no. 4 (October 2000): 383–400. http://dx.doi.org/10.1006/jsco.1999.0413.

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Kahle, Thomas, Ezra Miller, and Christopher O’Neill. "Irreducible decomposition of binomial ideals." Compositio Mathematica 152, no. 6 (April 1, 2016): 1319–32. http://dx.doi.org/10.1112/s0010437x16007272.

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Building on coprincipal mesoprimary decomposition [Kahle and Miller, Decompositions of commutative monoid congruences and binomial ideals, Algebra and Number Theory 8 (2014), 1297–1364], we combinatorially construct an irreducible decomposition of any given binomial ideal. In a parallel manner, for congruences in commutative monoids we construct decompositions that are direct combinatorial analogues of binomial irreducible decompositions, and for binomial ideals we construct decompositions into ideals that are as irreducible as possible while remaining binomial. We provide an example of a binomial ideal that is not an intersection of irreducible binomial ideals, thus answering a question of Eisenbud and Sturmfels [Binomial ideals, Duke Math. J. 84 (1996), 1–45].
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Gao, Xiao-Shan, Zhang Huang, and Chun-Ming Yuan. "Binomial difference ideals." Journal of Symbolic Computation 80 (May 2017): 665–706. http://dx.doi.org/10.1016/j.jsc.2016.07.029.

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Ojeda, Ignacio. "Binomial Canonical Decompositions of Binomial Ideals." Communications in Algebra 39, no. 10 (October 2011): 3722–35. http://dx.doi.org/10.1080/00927872.2010.511923.

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Kahle, Thomas. "Decompositions of binomial ideals." Journal of Software for Algebra and Geometry 4, no. 1 (2012): 1–5. http://dx.doi.org/10.2140/jsag.2012.4.1.

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Becker, Eberhard, Rudolf Grobe, and Michael Niermann. "Radicals of binomial ideals." Journal of Pure and Applied Algebra 117-118 (May 1997): 41–79. http://dx.doi.org/10.1016/s0022-4049(97)00004-2.

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Kahle, Thomas. "Decompositions of binomial ideals." Annals of the Institute of Statistical Mathematics 62, no. 4 (March 26, 2010): 727–45. http://dx.doi.org/10.1007/s10463-010-0290-9.

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Rauh, Johannes. "Generalized binomial edge ideals." Advances in Applied Mathematics 50, no. 3 (March 2013): 409–14. http://dx.doi.org/10.1016/j.aam.2012.08.009.

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Ene, Viviana, Giancarlo Rinaldo, and Naoki Terai. "Licci binomial edge ideals." Journal of Combinatorial Theory, Series A 175 (October 2020): 105278. http://dx.doi.org/10.1016/j.jcta.2020.105278.

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Dissertations / Theses on the topic "Binomial ideals"

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Mascia, Carla. "Ideals generated by 2-minors: binomial edge ideals and polyomino ideals." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/252052.

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Since the early 1990s, a classical object in commutative algebra has been the study of binomial ideals. A widely-investigated class of binomial ideals is the one containing those generated by a subset of 2-minors of an (m x n)-matrix of indeterminates. This thesis is devoted to illustrate some algebraic and homological properties of two classes of ideals of 2-minors: binomial edge ideals and polyomino ideals. Binomial edge ideals arise from finite graphs and their appeal results from the fact that their homological properties reflect nicely the combinatorics of the underlying graph. First, we focus on the binomial edge ideals of block graphs. We give a lower bound for their Castelnuovo-Mumford regularity by computing the two distinguished extremal Betti numbers of a new family of block graphs, called flower graphs. Moreover, we present a linear time algorithm to compute Castelnuovo-Mumford regularity and Krull dimension of binomial edge ideals of block graphs. Secondly, we consider some classes of Cohen-Macaulay binomial edge ideals. We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones, and we show the extremal Betti numbers of Cohen-Macaulay bipartite and fan graphs. In addition, we compute the Hilbert-Poincaré series of the binomial edge ideals of some Cohen-Macaulay bipartite graphs. Polyomino ideals arise from polyominoes, plane figures formed by joining one or more equal squares edge to edge. It is known that the polyomino ideal of simple polyominoes is prime. We consider multiply connected polyominoes, namely polyominoes with holes, and observe that the non-existence of a certain sequence of inner intervals of the polyomino, called zig-zag walk, gives a necessary condition for the primality of the polyomino ideal. Moreover, by computational approach, we prove that for all polyominoes with rank less than or equal to 14 the above condition is also sufficient. Lastly, we present an infinite class of prime polyomino ideals.
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Mascia, Carla. "Ideals generated by 2-minors: binomial edge ideals and polyomino ideals." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/252052.

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Since the early 1990s, a classical object in commutative algebra has been the study of binomial ideals. A widely-investigated class of binomial ideals is the one containing those generated by a subset of 2-minors of an (m x n)-matrix of indeterminates. This thesis is devoted to illustrate some algebraic and homological properties of two classes of ideals of 2-minors: binomial edge ideals and polyomino ideals. Binomial edge ideals arise from finite graphs and their appeal results from the fact that their homological properties reflect nicely the combinatorics of the underlying graph. First, we focus on the binomial edge ideals of block graphs. We give a lower bound for their Castelnuovo-Mumford regularity by computing the two distinguished extremal Betti numbers of a new family of block graphs, called flower graphs. Moreover, we present a linear time algorithm to compute Castelnuovo-Mumford regularity and Krull dimension of binomial edge ideals of block graphs. Secondly, we consider some classes of Cohen-Macaulay binomial edge ideals. We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones, and we show the extremal Betti numbers of Cohen-Macaulay bipartite and fan graphs. In addition, we compute the Hilbert-Poincaré series of the binomial edge ideals of some Cohen-Macaulay bipartite graphs. Polyomino ideals arise from polyominoes, plane figures formed by joining one or more equal squares edge to edge. It is known that the polyomino ideal of simple polyominoes is prime. We consider multiply connected polyominoes, namely polyominoes with holes, and observe that the non-existence of a certain sequence of inner intervals of the polyomino, called zig-zag walk, gives a necessary condition for the primality of the polyomino ideal. Moreover, by computational approach, we prove that for all polyominoes with rank less than or equal to 14 the above condition is also sufficient. Lastly, we present an infinite class of prime polyomino ideals.
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Shokrieh, Farbod. "Divisors on graphs, binomial and monomial ideals, and cellular resolutions." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/52176.

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We study various binomial and monomial ideals arising in the theory of divisors, orientations, and matroids on graphs. We use ideas from potential theory on graphs and from the theory of Delaunay decompositions for lattices to describe their minimal polyhedral cellular free resolutions. We show that the resolutions of all these ideals are closely related and that their Z-graded Betti tables coincide. As corollaries, we give conceptual proofs of conjectures and questions posed by Postnikov and Shapiro, by Manjunath and Sturmfels, and by Perkinson, Perlman, and Wilmes. Various other results related to the theory of chip-firing games on graphs also follow from our general techniques and results.
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Riderer, Lucia. "Numbers of generators of ideals in local rings and a generalized Pascal's Triangle." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2732.

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This paper defines generalized binomial coefficients and shows that they can be used to generate generalized Pascal's Triangles and have properties analogous to binomial coefficients. It uses the generalized binomial coefficients to compute the Dilworth number and the Sperner number of certain rings.
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Toman, Stefan [Verfasser], Ernst W. [Akademischer Betreuer] [Gutachter] Mayr, and Bruno [Gutachter] Buchberger. "Radicals of Binomial Ideals and Commutative Thue Systems / Stefan Toman ; Gutachter: Ernst W. Mayr, Bruno Buchberger ; Betreuer: Ernst W. Mayr." München : Universitätsbibliothek der TU München, 2017. http://d-nb.info/113701055X/34.

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De, Alba Casillas Hernan. "Nombres de Betti d'idéaux binomiaux." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENM043/document.

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Ha Minh Lam et M. Morales ont introduit une classe d'idéaux binomiaux qui est une extension binomiale d'idéaux monomiaux libres de carrés.Étant donné I un idéal monomial quadratique de k[x] libre de carrés et J une somme d'idéaux de scroll de k[z] qui satisfont certaines conditions, nous définissons l'extension binomiale de I comme B=I+J. Le sujet de cette thèse est d'étudier le nombre p plus grand tel que les sizygies de B son linéaires jusqu'au pas p-1. Sous certaines conditions d'ordre imposées sur les facettes du complexe de Stanley-Reisner de I nous obtiendrons un ordre > pour les variables de l'anneau de polynomes k[z]. Ensuite nous prouvons pour un calcul des bases de Gröbner que l'idéal initial in(B), sous l'ordre lexicographique induit par l'ordre de variables >, est quadratique libre de carrés. Nous montrerons que B est régulier si et seulement si I est 2-régulier. Dans le cas géneral, lorsque I n'est pas 2-régulier nous trouverons une borne pour l'entier q maximal qui satisfait que les premier q-1 sizygies de B son linéaires. En outre, en supossant que J est un idéal torique et en imposant des conditions supplémentaires, nous trouveron une borne supérieure pour l'entier q maximal qui satisfait que les premier q-1 sizygies de B son linéaires. En imposant des conditions supplémentaires, nous prouverons que les deux bornes sont égaux
Ha Minh Lam et M. Morales introduced a family of binomial ideals that are binomial extensions of square free monomial ideals. Let I be a square free monomial ideal of k[x] and J a sum of scroll ideals in k[z] with some extra conditions, we define the binomial extension of $I$ as $B=I+Jsubset sis$. The aim of this thesis is to study the biggest number p such that the syzygies of B are linear until the step p-1. Due to some order conditions given to the facets of the Stanley-Reisner complex of I we get an order > for the variables of the polynomial ring k[z]. By a calculation of the Gröbner basis of the ideal $B$ we obtain that the initial ideal in(B) is a square free monomial ideal. We will prove that B is 2-regular iff I is 2-regular. In the general case, wheter I is not 2-regular we will find a lower bound for the the maximal integer q which satisfies that the first q-1 sizygies of B are linear. On the other hand, wheter J is toric and supposing other conditions, we will find a upper bound for the integer q which satisfies that the first q-1 syzygies of B are linear. By given more conditions we will prove that the twobounds are equal
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ONeill, Christopher David. "Monoid Congruences, Binomial Ideals, and Their Decompositions." Diss., 2014. http://hdl.handle.net/10161/8786.

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This dissertation refines and extends the theory of mesoprimary decomposition, as introduced by Kahle and Miller. We begin with an overview of the existing theory of mesoprimary decomposition

in both the combinatorial setting of monoid congruences and the arithmetic setting of binomial ideals. We state all definitions and results that are relevant for subsequent chapters.

We classify redundant mesoprimary components in both the combinatorial and arithmetic settings. Kahle and Miller give a class of redundant components in each setting that are redundant in every mesoprimary decomposition. After identifying a further class of redundant components at the level of congruences, we give a condition on the associated monoid primes that guarantees the existence of unique irredundant mesoprimary decompositions in both settings.

We introduce soccular congruences as combinatorial approximations of irreducible binomial quotients and use the theory of mesoprimary decomposition to give a combinatorial method of constructing irreducible decompositions of binomial ideals. We also demonstrate a binomial ideal which does not admit a binomial irreducible decomposition, answering a long-standing problem of Eisenbud and Sturmfels.

We extend mesoprimary decomposition of monoid congruences to congruences on monoid modules. Much of the theory for monoid congruences extends to this new setting, including a characterization of mesoprimary monoid module congruences in terms of associated prime monoid congruences and a method for constructing coprincipal decompositions of monoid module congruences using key witnesses.

We conclude with a collection of open problems for future study.


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Varejão, Gonçalo Nuno Mota. "Eulerian Ideals and beyond." Master's thesis, 2021. http://hdl.handle.net/10316/95559.

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Dissertação de Mestrado em Matemática apresentada à Faculdade de Ciências e Tecnologia
O anel de polinómios K[x_1,...,x_n], com K um corpo, é um conceito importante na Álgebra Comutativa. Os matemáticos têm trabalhado com anéis de polinómios e os seus ideais desde o final do século XIX, mas a Álgebra Comutativa apenas se concretizou como um ramo da matemática no século XX. Foi em 1921, com o trabalho de Emmy Noether, que muitos dos atuais conceitos abstratos que estudamos em Álgebra Comutativa, ganharam a atenção da comunidade matemática. Hoje em dia, há uma nova área de investigação que combina a Álgebra Comutativa com a Combinatória, através do anel de polinómios. Neste trabalho, vamos estudar alguma da teoria necessária para compreender alguns conceitos deste ramo da matemática, que tem hoje o nome de Álgebra Comutativa Combinatória. Começamos por estudar propriedades gerais de módulos e de outros conceitos relacionados, como sequências exactas e módulos de sizígias. Explicamos como construir resoluções livres de um módulo e enunciamos o Teorema das Sizígias de Hilbert. Depois passamos para a teoria dos módulos graduados. Mostramos que os módulos de sizígias podem ser vistos como submódulos graduados, e definimos resoluções graduadas. Apresentamos também a sua construção, e de seguida enunciamos a versão graduada do Teorema das Sizígias de Hilbert. Terminamos o capítulo da teoria preliminar definindo a função de Hilbert, dando exemplos, e mostrando que esta é de tipo polinomial. Relativamente à Álgebra Comutativa Combinatória, vamos apresentar uma construção que liga as ferramentas algébricas mencionadas à teoria dos grafos, o ideal Euleriano de um grafo. Vamos apresentar os resultados e as demonstrações de Neves, Vaz Pinto, e Villarreal. Primeiro caracterizamos os geradores do ideal usando os subgrafos Eulerianos do grafo. Mostramos que o polinómio de Hilbert do módulo quociente pelo ideal Euleriano é constante, e estudamos o índice de regularidade deste módulo. Nesse estudo caracterizamos o índice de regularidade para grafos bipartidos, através das junções do grafo. De seguida estudamos T-junções e apresentamos a relação entre junção e T-junção. Estes resultados são depois usados para calcular, de forma explícita, o índice de regularidade para os grafos bipartidos completos, e Hamiltonianos bipartidos. Depois generalizamos a construção do ideal Euleriano para hipergrafos. Focamo-nos em hipergrafos k-uniformes, e generalizamos para estes os resultados apresentados para grafos. Em particular, caracterizamos o índice de regularidade para hipergrafos k-uniformes k-partidos, calculando-o para o caso k-partido completo.
The polynomial ring K[x_1,...,x_n], with K a field, is an important concept in commutative algebra. Mathematicians have been working with polynomial rings and their ideals since the late XIX century, but commutative algebra itself only came alive, as a field of mathematics, in the XX century. It was in 1921, with the work of Emmy Noether, that many of the current abstract concepts we study in commutative algebra drew the attention of the mathematical community. Nowadays there is a new area of research that combines commutative algebra and combinatorics through the polynomial ring. In this work we will study some of the theory necessary to comprehend many concepts of this field of mathematics, now called combinatorial commutative algebra. We begin by studying general properties of modules and other related concepts, such as exact sequences and syzygy modules. We explain how to construct a free resolution of a module and enunciate the Hilbert's Syzygy Theorem. Then we move on to the theory of graded modules. We show syzygy modules can be seen as graded submodules, and define graded resolutions. For these we will also give the construction, and then enunciate the graded version of the Syzygy Theorem of Hilbert. We end the chapter of the preliminary theory by defining the Hilbert function, giving examples, and showing it is a function of polynomial type. Regarding combinatorial commutative algebra, we will present one construction that connects the algebraic tools we mentioned before to the theory of graphs, the Eulerian ideal of a graph. We will present the results and proofs of Neves, Vaz Pinto, and Villarreal. We first characterize the generators of the ideal using the Eulerian subgraphs of the graph. We prove that the Hilbert polynomial of the quotient module by the Eulerian ideal is constant, and study the regularity index of this module. Then we present a characterization of this regularity index, for bipartite graphs, using the joins of the graph. After that, we study T-joins and present the connection between join and T-join. These results are then used to explicitly calculate the regularity index for the complete bipartite graphs, and Hamiltonian bipartite graphs. Afterwards, we generalize the construction of the Eulerian ideal for hypergraphs. We focus on k-uniform hypergraphs, and generalize for these the results presented for graphs. In particular, we characterize the regularity index for k-partite k-uniform hypergraphs, and calculate it for the complete k-partite case.
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Wang, Zhi-he, and 王智禾. "Binomial Ideals in Polynomial Rings and Laurent Polynomial Rings." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/24245686075866636502.

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碩士
國立中正大學
數學所
98
In this thesis, we study some properties of binomial ideals in polynomial rings and Laurent polynomial rings and find that there is a one-to-one cor- respondence between binomial ideals in Laurent polynomial rings and the partial character of sublattice in Zn . Moreover, we also prove that the radical of a binomial ideal in polynomial rings is still a binomial ideal.
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Books on the topic "Binomial ideals"

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Herzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. Binomial Ideals. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95349-6.

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Trends in number theory: Fifth Spanish meeting on number theory, July 8-12, 2013, Universidad de Sevilla, Sevilla, Spain. Providence, Rhode Island: American Mathematical Society, 2015.

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Herzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. Binomial Ideals. Springer, 2018.

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Herzog, Jürgen. Binomial Ideals. Springer, 2019.

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Current Trends on Monomial and Binomial Ideals. MDPI, 2020. http://dx.doi.org/10.3390/books978-3-03928-361-3.

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Wright, A. G. Statistical processes. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199565092.003.0004.

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Two statistical processes affect performance: one concerns photon detection at the photocathode (binomial); and the other, gain at each dynode (Poisson). The combined statistical processes dictate resolution, both timing and pulse height. They are best examined using generating functions that are both elegant and capable of providing answers more efficiently than traditional approaches. The requirement for steady and pulsed light sources is an important one for testing and setting up procedures. The use of moments to test the quality of performance is illustrated for a steady DC light source. Amplification provided by a dynode stack is a cascade process, leading to dispersion in gain, and is also ideally handled with generating functions. Theory is developed for essentially continuous pulse height distributions, such as those produced by a multichannel analyser. Arrival time statistics for scintillators are investigated analytically and by Monte Carlo simulation. Treatment is given for dead time and scaling.
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Pineda Buitrago, Sebastián, and José Sánchez Carbó, eds. Literatura aplicada en el siglo XXI: Ideas y prácticas. Editora Nómada, 2022. http://dx.doi.org/10.47377/litaplic.

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Compuesto por capítulos de diferentes especialistas en los estudios literarios que laboran en universidades de México, Europa y Estados Unidos, el libro Literatura aplicada en el siglo XXI: ideas y prácticas es el resultado de una invitación y de un esfuerzo para reflexionar sobre las posibilidades epistémicas del fenómeno literario como creación, recreación y programación. Parte de cuestionarse si el binomio clásico de estudiar/aprender ha perdido su sentido en la era de la tecnificación cibernética, es decir, de la inteligencia artificial y de la paulatina robotización del mundo. Puesto que los algoritmos ya leen y escriben automáticamente, y son capaces de combinaciones y hasta de generar narrativas, nos pareció necesaria una mayor sensibilización de la palabra consciente. Una reflexión de la educación poética para diferenciarnos de las máquinas y también para entender su funcionamiento, así como reestablecer la reflexión o diálogo de los creadores con los críticos, y de los promotores de lectura con los teóricos de la lectura. Tal restablecimiento debería ser el desafío de los estudios literarios (universitariamente entendidos) en lo que resta del siglo XXI. De esta forma, los ensayos aquí reunidos hacen referencia a autores y obras del siglo XX y aun de otras centurias, pero con la intención de reflexionar sobre su aplicación en lo que va del presente siglo.
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Keevak, Michael. How Did East Asians Become Yellow? Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190465285.003.0011.

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This chapter offers a brief historical intervention explaining the rise of the term yellow for racial thinking about Asians. Using his binomial nomenclature species-naming system, the Swedish taxonomist Carolus Linnaeus separated Homo sapiens into four continental types, with distinct colors assigned to each. Over two decades later the German anatomist Johann Friedrich Blumenbach also classified Asians as yellow in his five-race scheme. Although some early twentieth-century anthropologists claimed to have proven that Mongolians (Asians) were physically yellow in an attempt to place Asians lower than Europeans, the initial categorization of yellow had no visual or biological basis. As Asians continued to refuse to take part in Western systems (Christianity, international trade), Europeans' perceptions of Asians' skin color darkened. Moreover in the late eighteenth and early nineteenth century, the yellow idea began to spread to East Asian cultures themselves.
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Zangara, Juan Pablo. Clásico de clásicos: literatura, arte y mitología deportiva. Ediciones de Periodismo y Comunicación (EPC), 2021. http://dx.doi.org/10.35537/10915/131182.

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Este trabajo de Zangara (o esta reunión de trabajos) recorre la idea de lo clásico remando en un barco en el que el deporte –pasión de Zangara– corrobora, una vez más, que es un pasaporte posible para decodificar bastante humanidad. Zangara indaga y piensa sobre fútbol y sobre boxeo, sobre toros y sobre personas. Pero, en especial, indaga y piensa sobre otro once potente que le permite retratar la cancha de sociedades que fueron y de sociedades que son. Ahí van esos once (once que podrían ser más): los mitos, los héroes, la épica, lo sagrado, el primitivismo, la eternidad, la naturalización, lo sobrenatural, la carnalidad, la civilización y (para completar un binomio de amplias resonancias argentinas) la barbarie. <i>(del prólogo de Ariel Scher)</i>
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Book chapters on the topic "Binomial ideals"

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Herzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. "Binomial Edge Ideals and Related Ideals." In Binomial Ideals, 171–238. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95349-6_7.

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Herzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. "Polynomial Rings and Gröbner Bases." In Binomial Ideals, 3–34. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95349-6_1.

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Herzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. "Review of Commutative Algebra." In Binomial Ideals, 35–58. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95349-6_2.

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Herzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. "Introduction to Binomial Ideals." In Binomial Ideals, 61–86. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95349-6_3.

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Herzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. "Convex Polytopes and Unimodular Triangulations." In Binomial Ideals, 87–114. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95349-6_4.

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Herzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. "Edge Polytopes and Edge Rings." In Binomial Ideals, 117–40. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95349-6_5.

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Herzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. "Join-Meet Ideals of Finite Lattices." In Binomial Ideals, 141–70. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95349-6_6.

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Herzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. "Ideals Generated by 2-Minors." In Binomial Ideals, 239–70. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95349-6_8.

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Herzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. "Statistics." In Binomial Ideals, 271–305. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95349-6_9.

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Ene, Viviana, Jürgen Herzog, and Takayuki Hibi. "Koszul Binomial Edge Ideals." In Bridging Algebra, Geometry, and Topology, 125–36. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09186-0_8.

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Conference papers on the topic "Binomial ideals"

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KAREEM, SHADMAN. "Integer-valued polynomials and binomially Noetherian rings." In 3rd International Conference of Mathematics and its Applications. Salahaddin University-Erbil, 2020. http://dx.doi.org/10.31972/ticma22.07.

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A torsion free as a Z- module ring R with unit is said to be a binomial ring if it is preserved as binomial symbol (a¦i)≔(a(a-1)(a-2)…(a-(i-1)))/i!, for each a∈R and i ≥ 0. The polynomial ring of integer-valued in rational polynomial Q[X] is defined by Int (Z^X):={h∈Q[X]:h(Z^X)⊂Z} an important example for binomial ring and is non-Noetherian ring. In this paper the algebraic structure of binomial rings has been studied by their properties of binomial ideals. The notion of binomial ideal generated by a given set has been defined. Which allows us to define new class of Noetherian ring using binomial ideals, which we named it binomially Noetherian ring. One of main result the ring Int (Z^({x,y})) over variables x and y present as an example of that kind of class of Noetherian. In general the ring Int(Z^X) over the finite set of variables X and for a particular F subset in Z the rings Int(F^(〖{x〗_1,x_2,...,x_i} ),Z)={h∈Q[x_1,x_2,...,x_i ]:h(F^(〖{x〗_1,x_2,...,x_i} ))⊆ Z} both are presented as examples of that kind of class of Noetherian.
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Jinwang, Liu, Liu Zhuojun, Liu Xiaoqi, and Wang Mingsheng. "The membership problem for ideals of binomial skew polynomial rings." In the 2001 international symposium. New York, New York, USA: ACM Press, 2001. http://dx.doi.org/10.1145/384101.384127.

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Chen, Yu-Ao, and Xiao-Shan Gao. "Criteria for Finite Difference Gröbner Bases of Normal Binomial Difference Ideals." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3087604.3087615.

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Koppenhagen, Ulla, and Ernst W. Mayr. "An optimal algorithm for constructing the reduced Gröbner basis of binomial ideals." In the 1996 international symposium. New York, New York, USA: ACM Press, 1996. http://dx.doi.org/10.1145/236869.236899.

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Aoyama, Toru. "An Algorithm for Computing Minimal Associated Primes of Binomial Ideals without Producing Redundant Components." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3087604.3087644.

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Seredenciuc, Nadia-Laura. "Certainty and Uncertainty in Education - A Contemporary Challenge for Teachers." In ATEE 2020 - Winter Conference. Teacher Education for Promoting Well-Being in School. LUMEN Publishing, 2021. http://dx.doi.org/10.18662/lumproc/atee2020/31.

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This study is a reflection on educational reality based on certainty and uncertainty coordinates. Exploring the significance of the binomial reality, generated by the different degrees of certainty, perceived by the actors involved in teaching, the article proposes a few acting options, in order to develop an appropriate orientation of the teacher training process, in a contemporary society marked by the “certainty of uncertainty”. Embracing the unknown, coping with unfamiliar situations, reflecting constructively on one’s own mistakes, as part of a teacher daily activity, are generated by a genuine positioning towards uncertainty in education, raising it from the status of a problem to the hypostasis of an opportunity. Mapping uncertainty through resilience, building confidence in experiencing doubt, reshaping learning by daring to approach dilemmas and stepping out of inaction can be viewed as valid alternatives in developing a professional self in a changing environment. That claims a rethinking of teacher training in terms of developing abilities for sustaining appropriate responses and a proper understanding of the relationship between certainty and uncertainty in education, having the intention of building quality learning experiences. The concepts of choice and change are about to conquer the ideas of standards and stability in educational context as proofs of a renewed approach in order to delineate core drivers of human development in contemporaneity. That is why rethinking teacher training needs to focus on articulating the reflective practicing with experiencing a constant change, integrating the multiplicity of opportunities in a supportive learning environment for developing a global competence, in order to respond effectively to the contemporary challenges.
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