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Journal articles on the topic 'Binomial ideals'

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Author: Grafiati
Published: 11 March 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Kahle, Thomas, Camilo Sarmiento, and Tobias Windisch. "Parity binomial edge ideals." Journal of Algebraic Combinatorics 44, no. 1 (December 21, 2015): 99–117. http://dx.doi.org/10.1007/s10801-015-0657-3.

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12

Chaudhry, Faryal, Ahmet Dokuyucu, and Rida Irfan. "On the binomial edge ideals of block graphs." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 2 (June 1, 2016): 149–58. http://dx.doi.org/10.1515/auom-2016-0033.

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Abstract We find a class of block graphs whose binomial edge ideals have minimal regularity. As a consequence, we characterize the trees whose binomial edge ideals have minimal regularity. Also, we show that the binomial edge ideal of a block graph has the same depth as its initial ideal.
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13

Ene, Viviana, Jürgen Herzog, and Takayuki Hibi. "Cohen-Macaulay binomial edge ideals." Nagoya Mathematical Journal 204 (December 2011): 57–68. http://dx.doi.org/10.1215/00277630-1431831.

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14

Ene, Viviana, Jürgen Herzog, and Takayuki Hibi. "Cohen-Macaulay binomial edge ideals." Nagoya Mathematical Journal 204 (December 2011): 57–68. http://dx.doi.org/10.1017/s0027763000010394.

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15

OHSUGI, HIDEFUMI, and TAKAYUKI HIBI. "INDISPENSABLE BINOMIALS OF FINITE GRAPHS." Journal of Algebra and Its Applications 04, no. 04 (August 2005): 421–34. http://dx.doi.org/10.1142/s0219498805001265.

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A binomial f belonging to a toric ideal I is indispensable if, for any system [Formula: see text] of binomial generators of I, either f or -f belongs to [Formula: see text]. In the present paper, we study indispensable binomials of the toric ideals IG arising from a finite graph G. First, we show that the toric ideal IG arising from a finite graph G whose complementary graph is weakly chordal is generated by the indispensable binomials if and only if no complete graph of order ≥4 is a subgraph of G. Second, we completely classify indispensable binomials of the toric ideal IG arising from a finite graph G satisfying the odd cycle condition. Finally, the existence of indispensable binomials of IG will be discussed.
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16

Gross, Elizabeth, and Nicole Yamzon. "Binomial ideals of domino tilings." Discrete Mathematics 344, no. 11 (November 2021): 112530. http://dx.doi.org/10.1016/j.disc.2021.112530.

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17

Damadi, Hamid, and Farhad Rahmati. "Smoothness in Binomial Edge Ideals." Mathematics 4, no. 2 (June 1, 2016): 37. http://dx.doi.org/10.3390/math4020037.

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18

Eser, Zekiye Sahin, and Laura Felicia Matusevich. "Decompositions of cellular binomial ideals." Journal of the London Mathematical Society 94, no. 2 (July 2016): 409–26. http://dx.doi.org/10.1112/jlms/jdw012.

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19

de Alba, Hernán, and Marcel Morales. "Betti numbers of binomial ideals." Journal of Symbolic Computation 80 (May 2017): 387–402. http://dx.doi.org/10.1016/j.jsc.2016.06.001.

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20

Katsabekis, Anargyros. "Arithmetical rank of binomial ideals." Archiv der Mathematik 109, no. 4 (August 3, 2017): 323–34. http://dx.doi.org/10.1007/s00013-017-1071-y.

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21

Fischer, Klaus G., and Jay Shapiro. "Mixed matrices and binomial ideals." Journal of Pure and Applied Algebra 113, no. 1 (November 1996): 39–54. http://dx.doi.org/10.1016/0022-4049(95)00144-1.

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22

LÓPEZ, HIRAM H., and RAFAEL H. VILLARREAL. "COMPLETE INTERSECTIONS IN BINOMIAL AND LATTICE IDEALS." International Journal of Algebra and Computation 23, no. 06 (September 2013): 1419–29. http://dx.doi.org/10.1142/s0218196713500288.

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For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set-theoretic complete intersections. In characteristic zero, we show that an arbitrary lattice ideal which is a binomial set-theoretic complete intersection is a complete intersection.
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23

Matsuda, Kazunori, and Satoshi Murai. "Regularity bounds for binomial edge ideals." Journal of Commutative Algebra 5, no. 1 (March 2013): 141–49. http://dx.doi.org/10.1216/jca-2013-5-1-141.

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24

Sahin Eser, Zekiye, and Laura Felicia Matusevich. "Corrigendum: Decompositions of cellular binomial ideals." Journal of the London Mathematical Society 100, no. 2 (October 2019): 717–19. http://dx.doi.org/10.1112/jlms.12232.

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25

de Castilla, I. Ojeda Martínez, and R. Piedra Sánchez. "Index of nilpotency of binomial ideals." ACM SIGSAM Bulletin 33, no. 3 (September 1999): 18. http://dx.doi.org/10.1145/347127.360386.

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26

Mohammadi, Fatemeh, and Leila Sharifan. "Hilbert Function of Binomial Edge Ideals." Communications in Algebra 42, no. 2 (October 18, 2013): 688–703. http://dx.doi.org/10.1080/00927872.2012.721037.

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27

Kumar, Arvind, and Rajib Sarkar. "Hilbert series of binomial edge ideals." Communications in Algebra 47, no. 9 (March 26, 2019): 3830–41. http://dx.doi.org/10.1080/00927872.2019.1570241.

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28

Ojeda, Ignacio, and Ramón Piedra. "Index of nilpotency of binomial ideals." Journal of Algebra 255, no. 1 (September 2002): 135–47. http://dx.doi.org/10.1016/s0021-8693(02)00147-3.

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29

Saeedi Madani, Sara, and Dariush Kiani. "Binomial edge ideals of regularity 3." Journal of Algebra 515 (December 2018): 157–72. http://dx.doi.org/10.1016/j.jalgebra.2018.08.027.

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30

Eto, Kazufumi. "Binomial arithmetical rank of lattice ideals." manuscripta mathematica 109, no. 4 (December 1, 2002): 455–63. http://dx.doi.org/10.1007/s00229-002-0317-5.

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31

Kiani, Dariush, and Sara Saeedi Madani. "Binomial edge ideals with pure resolutions." Collectanea Mathematica 65, no. 3 (March 12, 2014): 331–40. http://dx.doi.org/10.1007/s13348-014-0107-x.

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32

Banerjee, Arindam, and Luis Núñez-Betancourt. "Graph connectivity and binomial edge ideals." Proceedings of the American Mathematical Society 145, no. 2 (August 18, 2016): 487–99. http://dx.doi.org/10.1090/proc/13241.

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33

Bolognini, Davide, Antonio Macchia, and Francesco Strazzanti. "Binomial edge ideals of bipartite graphs." European Journal of Combinatorics 70 (May 2018): 1–25. http://dx.doi.org/10.1016/j.ejc.2017.11.004.

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34

Shibuta, Takafumi, and Shunsuke Takagi. "Log canonical thresholds of binomial ideals." manuscripta mathematica 130, no. 1 (May 5, 2009): 45–61. http://dx.doi.org/10.1007/s00229-009-0270-7.

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35

Mascia, Carla, and Giancarlo Rinaldo. "Extremal Betti Numbers of Some Cohen–Macaulay Binomial Edge Ideals." Algebra Colloquium 28, no. 03 (July 26, 2021): 415–30. http://dx.doi.org/10.1142/s1005386721000328.

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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 some classes of Cohen–Macaulay binomial edge ideals: 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.
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36

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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37

Kumar, Arvind. "Lovász–Saks–Schrijver ideals and parity binomial edge ideals of graphs." European Journal of Combinatorics 93 (March 2021): 103274. http://dx.doi.org/10.1016/j.ejc.2020.103274.

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38

Bresinsky, H., F. Curtis, and J. Stückrad. "$\rho$-homogeneous binomial ideals and Patil bases." Rocky Mountain Journal of Mathematics 42, no. 3 (June 2012): 823–45. http://dx.doi.org/10.1216/rmj-2012-42-3-823.

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39

Ohtani, Masahiro. "Binomial Edge Ideals of Complete Multipartite Graphs." Communications in Algebra 41, no. 10 (October 3, 2013): 3858–67. http://dx.doi.org/10.1080/00927872.2012.680219.

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40

Rauf, Asia, and Giancarlo Rinaldo. "Construction of Cohen–Macaulay Binomial Edge Ideals." Communications in Algebra 42, no. 1 (October 18, 2013): 238–52. http://dx.doi.org/10.1080/00927872.2012.709569.

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41

Dokuyucu, Ahmet, Ajdin Halilovic, and Rida Irfan. "Gorenstein binomial edge ideals associated with scrolls." Communications in Algebra 45, no. 6 (October 7, 2016): 2602–12. http://dx.doi.org/10.1080/00927872.2016.1233219.

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42

Kesh, Deepanjan, and Shashank K. Mehta. "A saturation algorithm for homogeneous binomial ideals." ACM Communications in Computer Algebra 45, no. 1/2 (July 25, 2011): 121–22. http://dx.doi.org/10.1145/2016567.2016586.

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43

Kumar, Arvind. "Binomial edge ideals of generalized block graphs." International Journal of Algebra and Computation 30, no. 08 (August 28, 2020): 1537–54. http://dx.doi.org/10.1142/s0218196720500526.

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We classify generalized block graphs whose binomial edge ideals admit a unique extremal Betti number. We prove that the Castelnuovo–Mumford regularity of binomial edge ideals of generalized block graphs is bounded below by [Formula: see text], where [Formula: see text] is the number of minimal cut sets of the graph [Formula: see text] and obtain an improved upper bound for the regularity in terms of the number of maximal cliques and pendant vertices of [Formula: see text].
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44

Herzog, Jürgen, Takayuki Hibi, Freyja Hreinsdóttir, Thomas Kahle, and Johannes Rauh. "Binomial edge ideals and conditional independence statements." Advances in Applied Mathematics 45, no. 3 (September 2010): 317–33. http://dx.doi.org/10.1016/j.aam.2010.01.003.

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45

Ene, Viviana, and Andrei Zarojanu. "On the regularity of binomial edge ideals." Mathematische Nachrichten 288, no. 1 (April 25, 2014): 19–24. http://dx.doi.org/10.1002/mana.201300186.

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46

Ene, Viviana, Jürgen Herzog, Takayuki Hibi, and Ayesha Asloob Qureshi. "The binomial edge ideal of a pair of graphs." Nagoya Mathematical Journal 213 (March 2014): 105–25. http://dx.doi.org/10.1215/00277630-2389872.

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AbstractWe introduce a class of ideals generated by a set of 2-minors of an (m×n)-matrix of indeterminates indexed by a pair of graphs. This class of ideals is a natural common generalization of binomial edge ideals and ideals generated by adjacent minors. We determine the minimal prime ideals of such ideals and give a lower bound for their degree of nilpotency. In some special cases we compute their Gröbner basis and characterize unmixedness and Cohen–Macaulayness.
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47

Ene, Viviana, Jürgen Herzog, Takayuki Hibi, and Ayesha Asloob Qureshi. "The binomial edge ideal of a pair of graphs." Nagoya Mathematical Journal 213 (March 2014): 105–25. http://dx.doi.org/10.1017/s0027763000026192.

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AbstractWe introduce a class of ideals generated by a set of 2-minors of an (m×n)-matrix of indeterminates indexed by a pair of graphs. This class of ideals is a natural common generalization of binomial edge ideals and ideals generated by adjacent minors. We determine the minimal prime ideals of such ideals and give a lower bound for their degree of nilpotency. In some special cases we compute their Gröbner basis and characterize unmixedness and Cohen–Macaulayness.
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48

Mascia, Carla, and Giancarlo Rinaldo. "Krull dimension and regularity of binomial edge ideals of block graphs." Journal of Algebra and Its Applications 19, no. 07 (July 23, 2019): 2050133. http://dx.doi.org/10.1142/s0219498820501339.

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We give a lower bound for the Castelnuovo-Mumford regularity of binomial edge ideals of block graphs by computing the two distinguished extremal Betti numbers of a new family of block graphs, called flower graphs. Moreover, we present linear time algorithms to compute the Castelnuovo–Mumford regularity and the Krull dimension of binomial edge ideals of block graphs.
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49

Kahle, Thomas, and Ezra Miller. "Decompositions of commutative monoid congruences and binomial ideals." Algebra & Number Theory 8, no. 6 (October 2, 2014): 1297–364. http://dx.doi.org/10.2140/ant.2014.8.1297.

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50

Barile, Margherita. "On Ideals Generated by Monomials and One Binomial." Algebra Colloquium 14, no. 04 (December 2007): 631–38. http://dx.doi.org/10.1142/s1005386707000582.

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