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Статті в журналах з теми "Binomial ideals"
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.
Повний текст джерелаMartÍnez 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.
Повний текст джерелаKahle, 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.
Повний текст джерелаGao, 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.
Повний текст джерелаOjeda, 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.
Повний текст джерелаKahle, 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.
Повний текст джерелаBecker, 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.
Повний текст джерелаKahle, 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.
Повний текст джерелаRauh, 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.
Повний текст джерелаEne, 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.
Повний текст джерелаДисертації з теми "Binomial ideals"
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.
Повний текст джерелаMascia, 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.
Повний текст джерелаShokrieh, Farbod. "Divisors on graphs, binomial and monomial ideals, and cellular resolutions." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/52176.
Повний текст джерелаRiderer, 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.
Повний текст джерелаToman, 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.
Повний текст джерелаDe, Alba Casillas Hernan. "Nombres de Betti d'idéaux binomiaux." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENM043/document.
Повний текст джерелаHa 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
ONeill, Christopher David. "Monoid Congruences, Binomial Ideals, and Their Decompositions." Diss., 2014. http://hdl.handle.net/10161/8786.
Повний текст джерелаThis 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.
Dissertation
Varejão, Gonçalo Nuno Mota. "Eulerian Ideals and beyond." Master's thesis, 2021. http://hdl.handle.net/10316/95559.
Повний текст джерелаO 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.
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.
Повний текст джерела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.
Книги з теми "Binomial ideals"
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.
Повний текст джерелаTrends 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.
Знайти повний текст джерелаHerzog, Jürgen, Takayuki Hibi, and Hidefumi Ohsugi. Binomial Ideals. Springer, 2018.
Знайти повний текст джерелаHerzog, Jürgen. Binomial Ideals. Springer, 2019.
Знайти повний текст джерелаCurrent Trends on Monomial and Binomial Ideals. MDPI, 2020. http://dx.doi.org/10.3390/books978-3-03928-361-3.
Повний текст джерелаWright, A. G. Statistical processes. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199565092.003.0004.
Повний текст джерелаPineda 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.
Повний текст джерелаKeevak, Michael. How Did East Asians Become Yellow? Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190465285.003.0011.
Повний текст джерелаZangara, 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.
Повний текст джерелаЧастини книг з теми "Binomial ideals"
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.
Повний текст джерелаHerzog, 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.
Повний текст джерелаHerzog, 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.
Повний текст джерелаHerzog, 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.
Повний текст джерелаHerzog, 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.
Повний текст джерелаHerzog, 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.
Повний текст джерелаHerzog, 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.
Повний текст джерелаHerzog, 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.
Повний текст джерелаHerzog, 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.
Повний текст джерелаEne, 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.
Повний текст джерелаТези доповідей конференцій з теми "Binomial ideals"
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.
Повний текст джерелаJinwang, 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.
Повний текст джерелаChen, 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.
Повний текст джерелаKoppenhagen, 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.
Повний текст джерелаAoyama, 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.
Повний текст джерелаSeredenciuc, 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.
Повний текст джерела