Relevant bibliographies by topics / Binomial edge ideals

Academic literature on the topic 'Binomial edge ideals'

Author: Grafiati
Published: 11 March 2023

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Journal articles on the topic "Binomial edge ideals"

1

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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Binomial edge ideals"

1

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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2

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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Book chapters on the topic "Binomial edge ideals"

1

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. "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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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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Saeedi Madani, Sara. "Binomial Edge Ideals: A Survey." In Springer Proceedings in Mathematics & Statistics, 83–94. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90493-1_4.

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Ene, Viviana, and Jürgen Herzog. "On the Symbolic Powers of Binomial Edge Ideals." In Combinatorial Structures in Algebra and Geometry, 43–50. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52111-0_4.

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