Results 11 to 20 of about 569 (30)
On certain equidimensional polymatroidal ideals [PDF]
, 2015 The class of equidimensional polymatroidal ideals are studied. In particular, we show that an unmixed polymatroidal ideal is connected in codimension one if and only if it is Cohen-Macaulay.
Bandari, Somayeh, Jafari, Raheleh
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Forum of Mathematics, SigmaThe study of Koszul binomial edge ideals was initiated by V. Ene, J. Herzog, and T. Hibi in 2014, who found necessary conditions for Koszulness. The binomial edge ideal $J_G$ associated to a finite simple graph G is always generated by quadrics ...
Adam LaClair +3 more
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Ap\'ery sets of shifted numerical monoids
, 2018 A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid $S$, consider the family of "shifted" monoids $M_n$ obtained by adding $n$ to each generator of $S$. In this paper, we characterize the Ap\'ery set of $M_n$
O'Neill, Christopher, Pelayo, Roberto
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Matroid toric ideals: complete intersection, minors and minimal systems of generators [PDF]
, 2015 In this paper, we investigate three problems concerning the toric ideal associated to a matroid. Firstly, we list all matroids $\mathcal M$ such that its corresponding toric ideal $I_{\mathcal M}$ is a complete intersection.
Alfonsín, Jorge Luis Ramírez +1 more
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Componentwise linearity of ideals arising from graphs [PDF]
, 2008 Let $G$ be a simple undirected graph on $n$ vertices. Francisco and Van Tuyl have shown that if $G$ is chordal, then $\bigcap_{\{x_i,x_j\}\in E_G} < x_i,x_j>$ is componentwise linear.
Emtander, E., Quinonez, V. Crispin
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A note on the regularity of Hibi rings [PDF]
, 2014 We compute the regularity of the Hibi ring of any finite distributive lattice in terms of its poset of join irreducible elements.Comment: 5 pages, 2 ...
Ene, Viviana +2 more
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Hilbert series of modules over positively graded polynomials rings [PDF]
, 2016 In this note, we give examples of formal power series satisfying certain conditions that cannot be realized as Hilbert series of finitely generated modules.
Katthän, Lukas +2 more
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Certain Classes of Cohen-Macaulay Multipartite Graphs
, 2018 The Cohen-Macaulay property of a graph arising from a poset has been studied by various authors. In this article, we study the Cohen-Macaulay property of a graph arising from a family of reflexive and antisymmetric relations on a set.
Kumar, Ajay, Kumar, Rajiv
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On the Hilbert series of vertex cover algebras of unmixed bipartite graphs [PDF]
, 2010 We compute the reduced Gr\"{o}bner basis of the toric ideal with respect to a suitable monomial order and we study the Hilbert series of the vertex cover algebra $A(G)$, where $G$ is an unmixed bipartite graph without isolated vertices.Comment: 8 ...
Ion, Cristian
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Candidates for non-zero Betti numbers of monomial ideals
, 2016 Let $I$ be a monomial ideal in the polynomial ring $S$ generated by elements of degree at most $d$. In this paper, it is shown that, if the $i$-th syzygy of $I$ has no element of degrees $j, \ldots, j+(d-1)$ (where $j \geq i+d$), then $(i+1)$-syzygy of ...
Pour, Ali Akbar Yazdan
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