Results 11 to 20 of about 1,194,320 (236)
Binomial edge ideals of bipartite graphs [PDF]
European Journal of Combinatorics, 2018 We classify the bipartite graphs $G$ whose binomial edge ideal $J_G$ is Cohen-Macaulay. The connected components of such graphs can be obtained by gluing a finite number of basic blocks with two operations. In this context we prove the converse of a well-known result due to Hartshorne, showing that the Cohen-Macaulayness of these ideals is equivalent ...
Davide Bolognini +2 more
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Generalized binomial edge ideals [PDF]
Advances in Applied Mathematics, 2013 6 pages.
Rauh, Johannes, Johannes Rauh
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On the binomial edge ideals of block graphs
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 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.
Chaudhry Faryal +2 more
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Binomial Edge Ideals of Weakly Closed Graphs
International Mathematics Research Notices, 2022 Abstract Closed graphs have been characterized by Herzog et al. as the graphs whose binomial edge ideals have a quadratic Gröbner basis with respect to a diagonal term order. In this paper, we focus on a generalization of closed graphs, namely weakly closed graphs (or co-comparability graphs).
Seccia, Lisa
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Binomial edge ideals and conditional independence statements [PDF]
Advances in Applied Mathematics, 2010 We introduce binomial edge ideals attached to a simple graph $G$ and study their algebraic properties. We characterize those graphs for which the quadratic generators form a Gröbner basis in a lexicographic order induced by a vertex labeling. Such graphs are chordal and claw-free. We give a reduced squarefree Gröbner basis for general $G$.
Jürgen Herzog +4 more
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On the symbolic F-splitness of binomial edge ideals [PDF]
Journal of Pure and Applied AlgebraWe study the symbolic $F$-splitness of families of binomial edge ideals. We also study the strong $F$-regularity of the symbolic blowup algebras of families of binomial edge ideals. We make use of Fedder-like criteria and combinatorial properties of the graphs associated to the binomial edge ideals in order to approach the aforementioned scenarios.
Ramírez-Moreno, Pedro
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Multidegrees of binomial edge ideals [PDF]
Communications in AlgebraLet $G$ be a simple graph with binomial edge ideal $J_G$. We prove how to calculate the multidegree of $J_G$ based on combinatorial properties of $G$. In particular, we study the set $S_{\min}(G)$ defined as the collection of subsets of vertices whose prime ideals have minimum codimension.
Cooper, Jacob, Leventhal, Ethan
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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
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Binomial edge ideals of unicyclic graphs [PDF]
International Journal of Algebra and Computation, 2021 Let [Formula: see text] be a connected graph on the vertex set [Formula: see text]. Then [Formula: see text]. In this paper, we prove that if [Formula: see text] is a unicyclic graph, then the depth of [Formula: see text] is bounded below by [Formula: see text]. Also, we characterize [Formula: see text] with [Formula: see text] and [Formula: see text].
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On the hilbert series of binomial edge ideals of generalized trees [PDF]
Transactions on Combinatorics, 2017 In this paper we introduce the concept of generalized trees and compute the Hilbert series of their binomial edge ideals.
Mahdis Saeedi, Farhad Rahmati
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