Journal articles: 'Generic initial ideals'

1

Caviglia, Giulio, and Enrico Sbarra. "Zero-generic initial ideals." Manuscripta Mathematica 148, no. 3-4 (May 6, 2015): 507–20. http://dx.doi.org/10.1007/s00229-015-0748-4.

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2

Bigatti, A. M., A. Conca, and L. Robbiano. "Generic Initial Ideals and Distractions." Communications in Algebra 33, no. 6 (May 2005): 1709–32. http://dx.doi.org/10.1081/agb-200058217.

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3

Draisma, Jan, Michał Lasoń, and Anton Leykin. "Stillman’s conjecture via generic initial ideals." Communications in Algebra 47, no. 6 (April 16, 2019): 2384–95. http://dx.doi.org/10.1080/00927872.2019.1574806.

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4

Murai, Satoshi. "Generic initial ideals and squeezed spheres." Advances in Mathematics 214, no. 2 (October 2007): 701–29. http://dx.doi.org/10.1016/j.aim.2007.03.004.

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5

Murai, Satoshi, and Pooja Singla. "Rigidity of Linear Strands and Generic Initial Ideals." Nagoya Mathematical Journal 190 (2008): 35–61. http://dx.doi.org/10.1017/s0027763000009557.

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Let K be a field, S a polynomial ring and E an exterior algebra over K, both in a finite set of variables. We study rigidity properties of the graded Betti numbers of graded ideals in S and E when passing to their generic initial ideals. First, we prove that if the graded Betti numbers for some i > 1 and k ≥ 0, then for all q ≥ i, where I ⊂ S is a graded ideal. Second, we show that if for some i > 1 and k ≥ 0, then for all q ≥ 1, where I ⊂ E is a graded ideal. In addition, it will be shown that the graded Betti numbers for all i ≥ 1 if and only if I(k) and I(k+1) have a linear resolution. Here I(d) is the ideal generated by all homogeneous elements in I of degree d, and R can be either the polynomial ring or the exterior algebra.

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6

DANIŞ, Bekir. "A short note on generic initial ideals." TURKISH JOURNAL OF MATHEMATICS 45, no. 3 (May 20, 2021): 1444–48. http://dx.doi.org/10.3906/mat-2008-106.

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7

Danış, Bekir, and Müfit Sezer. "Generic initial ideals of modular polynomial invariants." Journal of Pure and Applied Algebra 224, no. 6 (June 2020): 106255. http://dx.doi.org/10.1016/j.jpaa.2019.106255.

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8

Conca, Aldo, and Jessica Sidman. "Generic initial ideals of points and curves." Journal of Symbolic Computation 40, no. 3 (September 2005): 1023–38. http://dx.doi.org/10.1016/j.jsc.2005.01.009.

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9

Àlvarez Montaner, Josep. "Local cohomology of binomial edge ideals and their generic initial ideals." Collectanea Mathematica 71, no. 2 (September 29, 2019): 331–48. http://dx.doi.org/10.1007/s13348-019-00268-z.

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10

Kaveh, Kiumars, Christopher Manon, and Takuya Murata. "Generic tropical initial ideals of Cohen-Macaulay algebras." Journal of Pure and Applied Algebra 225, no. 11 (November 2021): 106713. http://dx.doi.org/10.1016/j.jpaa.2021.106713.

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11

Zaare-Nahandi, Rahim. "Betti Numbers of Transversal Monomial Ideals." Algebra Colloquium 18, spec01 (December 2011): 925–36. http://dx.doi.org/10.1142/s1005386711000800.

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In this paper, by a modification of a previously constructed minimal free resolution for a transversal monomial ideal, the Betti numbers of this ideal is explicitly computed. For convenient characteristics of the ground field, up to a change of coordinates, the ideal of t-minors of a generic pluri-circulant matrix is a transversal monomial ideal. Using a Gröbner basis for this ideal, it is shown that the initial ideal of a generic pluri-circulant matrix is a stable monomial ideal when the matrix has two square blocks. By means of the Eliahou-Kervaire resolution for stable monomial ideals, the Betti numbers of this initial ideal is computed and it is proved that for some significant values of t, this ideal has the same Betti numbers as the corresponding transversal monomial ideal. The ideals treated in this paper naturally arise in the study of generic singularities of algebraic varieties.

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12

Cho, Hyang Mi, Young Hyun Cho, and Jung Pil Park. "Generic Initial Ideals of Arithmetically Cohen–Macaulay Projective Subschemes." Communications in Algebra 35, no. 7 (June 15, 2007): 2281–97. http://dx.doi.org/10.1080/00927870701329126.

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13

Harima, Tadahito, and Akihito Wachi. "Generic Initial Ideals, Graded Betti Numbers, andk-Lefschetz Properties." Communications in Algebra 37, no. 11 (November 11, 2009): 4012–25. http://dx.doi.org/10.1080/00927870802502753.

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14

Ahn, Jeaman, Young Hyun Cho, and Jung Pil Park. "Generic initial ideals of Artinian ideals having Lefschetz properties or the strong Stanley property." Journal of Algebra 318, no. 2 (December 2007): 589–606. http://dx.doi.org/10.1016/j.jalgebra.2007.09.016.

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15

Cho, Young Hyun, and Jung Pil Park. "Conditions for generic initial ideals to be almost reverse lexicographic." Journal of Algebra 319, no. 7 (April 2008): 2761–71. http://dx.doi.org/10.1016/j.jalgebra.2008.01.014.

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16

Ahn, Jeaman, Sijong Kwak, and YeongSeok Song. "Generic initial ideals of singular curves in graded lexicographic order." Journal of Algebra 372 (December 2012): 584–94. http://dx.doi.org/10.1016/j.jalgebra.2012.09.011.

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17

Caviglia, Giulio, and Enrico Sbarra. "Generic circuits sets and general initial ideals with respect to weights." Journal of Commutative Algebra 5, no. 1 (March 2013): 49–62. http://dx.doi.org/10.1216/jca-2013-5-1-49.

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18

Mayes, Sarah. "The generic initial ideals of powers of a 2-complete intersection." Journal of Commutative Algebra 7, no. 1 (March 2015): 55–75. http://dx.doi.org/10.1216/jca-2015-7-1-55.

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19

Harima, Tadahito, Sho Sakaki, and Akihito Wachi. "Generic initial ideals of some monomial complete intersections in four variables." Archiv der Mathematik 94, no. 2 (January 20, 2010): 129–37. http://dx.doi.org/10.1007/s00013-009-0088-2.

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20

Conca, A., E. De Negri, and E. Gorla. "Universal Gröbner Bases and Cartwright–Sturmfels Ideals." International Mathematics Research Notices 2020, no. 7 (April 25, 2018): 1979–91. http://dx.doi.org/10.1093/imrn/rny075.

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Abstract The main theoretical contribution of the paper is the description of two classes of multigraded ideals named after Cartwright and Sturmfels and the study of their surprising properties. Among other things we prove that these classes of ideals have very special multigraded generic initial ideals and are closed under several operations including arbitrary multigraded hyperplane sections. As a main application we describe the universal Gröbner basis of the ideal of maximal minors and the ideal of 2-minors of a multigraded matrix of linear forms generalizing earlier results of various authors including Bernstein, Sturmfels, Zelevinsky, and Boocher.

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21

Hyeon, Donghoon, and Hyungju Park. "Grothendieck–Plücker Images of Hilbert Schemes are Degenerate." Proceedings of the Edinburgh Mathematical Society 62, no. 1 (August 22, 2018): 47–60. http://dx.doi.org/10.1017/s0013091518000421.

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AbstractWe study the decompositions of Hilbert schemes induced by the Schubert cell decomposition of the Grassmannian variety and show that Hilbert schemes admit a stratification into locally closed subschemes along which the generic initial ideals remain the same. We give two applications. First, we give completely geometric proofs of the existence of the generic initial ideals and of their Borel fixed properties. Second, we prove that when a Hilbert scheme of non-constant Hilbert polynomial is embedded by the Grothendieck–Plücker embedding of a high enough degree, it must be degenerate.

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22

Murai, Satoshi. "Generic initial ideals and exterior algebraic shifting of the join of simplicial complexes." Arkiv för Matematik 45, no. 2 (October 2007): 327–36. http://dx.doi.org/10.1007/s11512-006-0030-9.

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23

Ahn, Jeaman, and Yong Su Shin. "Generic initial ideals and graded Artinian-level algebras not having the Weak-Lefschetz Property." Journal of Pure and Applied Algebra 210, no. 3 (September 2007): 855–79. http://dx.doi.org/10.1016/j.jpaa.2006.12.003.

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24

Murai, Satoshi, and Takayuki Hibi. "Gin and lex of certain monomial ideals." MATHEMATICA SCANDINAVICA 99, no. 1 (September 1, 2006): 76. http://dx.doi.org/10.7146/math.scand.a-15000.

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Let $A = K[x_1,\ldots, x_n]$ denote the polynomial ring in $n$ variables over a field $K$ of characteristic $0$ with each $\deg x_i = 1$. Given arbitrary integers $i$ and $j$ with $2 \leq i \leq n$ and $3 \leq j \leq n$, we will construct a monomial ideal $I \subset A$ such that (i) $\beta_k(I) < \beta_k(\mathrm{Gin}(I))$ for all $k < i$, (ii) $\beta_i(I)= \beta_i(\mathrm{Gin}(I))$, (iii) $\beta_\ell((\mathrm{Gin}(I)) < \beta_\ell((\mathrm{Lex}(I))$ for all $\ell < j$ and (iv) $\beta_j(\mathrm{Gin}(I)) = \beta_j(\mathrm{Lex}(I))$, where $\mathrm{Gin}(I)$ is the generic initial ideal of $I$ with respect to the reverse lexicographic order induced by $x_1 > \cdots > x_n$ and where $\mathrm{Lex}(I)$ is the lexsegment ideal with the same Hilbert function as $I$.

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25

Stracke, Christian M., Daniel Burgos, Gema Santos-Hermosa, Aras Bozkurt, Ramesh Chander Sharma, Cécile Swiatek Cassafieres, Andreia Inamorato dos Santos, et al. "Responding to the Initial Challenge of the COVID-19 Pandemic: Analysis of International Responses and Impact in School and Higher Education." Sustainability 14, no. 3 (February 7, 2022): 1876. http://dx.doi.org/10.3390/su14031876.

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This paper presents and analyses solutions where open education and open science were utilised to reduce the impact of the COVID-19 pandemic on education. The COVID-19 outbreak and associated lockdowns created huge challenges in school and higher education, demanding sudden responses which aimed to sustain pedagogical quality. Responses have varied from conservative to radically innovative. Universally, the COVID-19 pandemic disrupted and shocked societies worldwide, and education systems were on the front line. The lockdowns largely stopped face-to-face and formal education in almost all countries, and in most cases, distance learning soon became the ‘new normal’. A central challenge concerned sustaining educational visions and ideals in such circumstances. To better understand the state of the art in the educational landscape, we collected case studies from 13 countries during the first year of the pandemic starting on 11 March 2020 (when the World Health Organization declared a pandemic). This paper presents summaries of the full country reports that were collected and describe lessons learned. Our overall aim was to identify good practices and recommendations from the collected case studies that can be taken forward in the future. We categorised the responses on the three generic educational levels (macro, meso and micro) and identified seven key aspects and trends that are valid for all or most countries: (1) formal education at a distance for first time; (2) similar approaches for formal education; (3) missing infrastructure and sharing open educational resources; (4) diverse teaching and learning methods and practices; (5) open education and access to open educational resources; (6) urgent need for professional development and training for teachers and (7) assessing and monitoring learning environments, teachers and students. Finally, we identified key recommendations on how open education and open science can benefit formal education in schools and universities in the future, namely, improved awareness of open educational practices, provision of ICT infrastructure, embracing and sustaining the practice of open access publications and OERs, capacity building for stakeholders and finally encouraging research and development in the area of open education and open science. We found significant evidence for the proposition that open education and open science can support both traditional face-to-face and distance learning.

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26

Bertone, Cristina, Francesca Cioffi, and Margherita Roggero. "Double-generic initial ideal and Hilbert scheme." Annali di Matematica Pura ed Applicata (1923 -) 196, no. 1 (March 1, 2016): 19–41. http://dx.doi.org/10.1007/s10231-016-0560-0.

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27

Fløystad, Gunnar. "Higher initial ideals of homogeneous ideals." Memoirs of the American Mathematical Society 134, no. 638 (1998): 0. http://dx.doi.org/10.1090/memo/0638.

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28

Fløystad, Gunnar. "A property deducible from the generic initial ideal." Journal of Pure and Applied Algebra 136, no. 2 (March 1999): 127–40. http://dx.doi.org/10.1016/s0022-4049(97)00165-5.

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29

Trung, Van Duc. "The initial ideal of generic sequences and Fröberg's Conjecture." Journal of Algebra 524 (April 2019): 79–96. http://dx.doi.org/10.1016/j.jalgebra.2019.01.011.

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30

Constantinescu, Alexandru, Emanuela De Negri, and Matteo Varbaro. "Singularities and radical initial ideals." Bulletin of the London Mathematical Society 52, no. 4 (June 28, 2020): 674–86. http://dx.doi.org/10.1112/blms.12358.

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31

Kalkbrener, M., and B. Sturmfels. "Initial Complexes of Prime Ideals." Advances in Mathematics 116, no. 2 (December 1995): 365–76. http://dx.doi.org/10.1006/aima.1995.1071.

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32

Ho\c{s}ten, Serkan, and Rekha R. Thomas. "The associated primes of initial ideals of lattice ideals." Mathematical Research Letters 6, no. 1 (1999): 83–97. http://dx.doi.org/10.4310/mrl.1999.v6.n1.a6.

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33

Conca, Aldo. "Reduction numbers and initial ideals." Proceedings of the American Mathematical Society 131, no. 4 (June 12, 2002): 1015–20. http://dx.doi.org/10.1090/s0002-9939-02-06607-8.

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34

Ohsugi, Hidefumi, and Takayuki Hibi. "Quadratic initial ideals of root systems." Proceedings of the American Mathematical Society 130, no. 7 (December 27, 2001): 1913–22. http://dx.doi.org/10.1090/s0002-9939-01-06411-5.

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35

Fløystad, Gunnar, and Mark L. Green. "The information encoded in initial ideals." Transactions of the American Mathematical Society 353, no. 4 (November 29, 2000): 1427–53. http://dx.doi.org/10.1090/s0002-9947-00-02737-9.

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36

Nurlanbekova, Y. K., and M. K. Suranshieva. "FEATURES OF THE FORMATION OF INITIAL IDEAS ABOUT ECONOMIC CULTURE IN PRESCHOOL ORGANIZATIONS." Bulletin of the Korkyt Ata Kyzylorda University 60, no. 1 (2022): 208–14. http://dx.doi.org/10.52081/bkaku.2022.v60.i1.027.

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The article focuses on the relevance of the formation of initial ideas about economic culture of preschoolers as an important component of the holistic development of personality in modern society. Economic culture is a part of the general human culture that influences economic policy in the state, the efficiency of work in society, and the well-being of each family. The formation of an economic culture among older preschoolers is relevant, modern and necessary.The theoretical context of the economic development of a preschooler’s personality testifies to the importance of the problem under consideration. The theoretical aspects of the essence of the problem of economic literacy of children at the stage of preschool childhood have been revealed in the article. In the process of organizing the experimental part of the study, the authors paid special attention to the attitude of teachers of preschool educational organizations to the problem of the formation of economic culture among preschoolers, since the teacher is the main figure of the pedagogical process and a decisive factor in economic education.

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37

Al-Ayyoub, Ibrahim. "The Ratliff-Rush Closure of Initial Ideals of Certain Prime Ideals." Rocky Mountain Journal of Mathematics 40, no. 4 (August 2010): 1085–93. http://dx.doi.org/10.1216/rmj-2010-40-4-1085.

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38

Ohsugi, Hidefumi, and Takayuki Hibi. "Compressed polytopes, initial ideals and complete multipartite graphs." Illinois Journal of Mathematics 44, no. 2 (June 2000): 391–406. http://dx.doi.org/10.1215/ijm/1255984847.

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39

Eisenbud, D., A. Reeves, and B. Totaro. "Initial Ideals, Veronese Subrings, and Rates of Algebras." Advances in Mathematics 109, no. 2 (December 1994): 168–87. http://dx.doi.org/10.1006/aima.1994.1085.

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40

Trung, Ngô Viêt. "Evaluations of initial ideals and Castelnuovo-Mumford regularity." Proceedings of the American Mathematical Society 130, no. 5 (October 5, 2001): 1265–74. http://dx.doi.org/10.1090/s0002-9939-01-06216-5.

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41

Jonsson, Jakob, and Volkmar Welker. "A spherical initial ideal for Pfaffians." Illinois Journal of Mathematics 51, no. 4 (October 2007): 1397–407. http://dx.doi.org/10.1215/ijm/1258138551.

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42

Bruns, Winfried, Tim Römer, and Attila Wiebe. "Initial algebras of determinantal rings, Cohen-Macaulay and Ulrich ideals." Michigan Mathematical Journal 53, no. 1 (April 2005): 71–81. http://dx.doi.org/10.1307/mmj/1114021085.

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43

Notari, R., and M. L. Spreafico. "A stratification of Hilbert schemes by initial ideals and applications." manuscripta mathematica 101, no. 4 (2000): 429. http://dx.doi.org/10.1007/s002290050225.

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44

Lindner, Felicitas. "Finite numbers of initial ideals in non-Noetherian polynomial rings." Proceedings of the American Mathematical Society 146, no. 9 (April 26, 2018): 3721–33. http://dx.doi.org/10.1090/proc/14082.

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45

Puttinger, Heidi. "Peritonealdialyse – ein ideales initiales Dialyseverfahren." Wiener Medizinische Wochenschrift 163, no. 11-12 (June 2013): 271–79. http://dx.doi.org/10.1007/s10354-013-0200-x.

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46

Ohsugi, Hidefumi, and Takayuki Hibi. "Convex polytopes all of whose reverse lexicographic initial ideals are squarefree." Proceedings of the American Mathematical Society 129, no. 9 (January 18, 2001): 2541–46. http://dx.doi.org/10.1090/s0002-9939-01-05853-1.

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47

Ramos, Zaqueu, and Aron Simis. "Homaloidal nets and ideals of fat points II: Subhomaloidal nets." International Journal of Algebra and Computation 27, no. 06 (September 2017): 677–715. http://dx.doi.org/10.1142/s0218196717500333.

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This work is a natural sequel to a previous paper by the authors in that it tackles problems of the same nature. Here, one aims at the ideal theoretic and homological properties of an ideal of general plane fat points for which the corresponding second symbolic power has virtual multiplicities of a proper homaloidal type. For this purpose, one carries a detailed examination of the underlying linear system at the initial degree, where a good deal of the results depends on the method of the classical arithmetic quadratic transformations of Hudson–Nagata. A subsidiary guide to understand these ideals through their initial linear systems has been supplied by questions of birationality with source [Formula: see text] and target higher dimensional spaces. This leads, in particular, to the retrieval of birational maps studied by Geramita–Gimigliano–Pitteloud, including a few of the celebrated Bordiga–White parameterizations.

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48

Ma, Rongchao. "Vortex penetration and flux relaxation with arbitrary initial conditions in non-ideal and ideal superconductors." Journal of Applied Physics 109, no. 10 (May 15, 2011): 103910. http://dx.doi.org/10.1063/1.3590148.

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49

Hoa, Lê Tuân. "Finiteness of Hilbert functions and bounds for Castelnuovo-Mumford regularity of initial ideals." Transactions of the American Mathematical Society 360, no. 09 (April 4, 2008): 4519–40. http://dx.doi.org/10.1090/s0002-9947-08-04424-3.

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50

Fay‐Ramirez, Suzanna. "Therapeutic Jurisprudence in Practice: Changes in Family Treatment Court Norms Over Time." Law & Social Inquiry 40, no. 01 (2015): 205–36. http://dx.doi.org/10.1111/lsi.12067.

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Family treatment court (FTC) is an example of an increasing number of problem‐centered courts currently operating in the United States. Problem‐centered courts such as FTC encompass the ideas of therapeutic jurisprudence but operate within the broader court system. Presented are the results of an FTC case study that seeks to understand the evolution of courtroom norms and practice over time. Observations of courtroom interactions and interviews with courtroom personnel show that initial observations are consistent with the ideals of therapeutic jurisprudence. However, over time, daily demands and pressures on the courtroom undermine the therapeutic approach.

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Journal articles on the topic 'Generic initial ideals'

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