共查询到20条相似文献,搜索用时 15 毫秒
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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. 相似文献
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《Mathematische Nachrichten》2018,291(1):28-40
We study the equality of the extremal Betti numbers of the binomial edge ideal and those of its initial ideal for a closed graph G. We prove that in some cases there is a unique extremal Betti number for and as a consequence there is a unique extremal Betti number for and these extremal Betti numbers are equal. 相似文献
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Giuseppe Valla 《Proceedings of the American Mathematical Society》2005,133(1):57-63
In this paper we compute the graded Betti numbers of certain monomial ideals that are not stable. As a consequence we prove a conjecture, stated by G. Fatabbi, on the graded Betti numbers of two general fat points in
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Nursel Erey 《代数通讯》2018,46(9):4007-4020
We show that if G is a gap-free and diamond-free graph, then I(G)s has a linear minimal free resolution for every s≥2. 相似文献
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We study the regularity of binomial edge ideals. For a closed graph G we show that the regularity of the binomial edge ideal coincides with the regularity of and can be expressed in terms of the combinatorial data of G. In addition, we give positive answers to Matsuda‐Murai conjecture 8 for some classes of graphs. 相似文献
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In this paper, we compute depth and Stanley depth for the quotient ring of the edge ideal associated to a square path on n vertices. We also compute depth and Stanley depth for the quotient ring of the edge ideal associated to a square cycle on n vertices, when n≡0,3,4( mod 5), and give tight bounds when n≡1,2( mod 5). We also prove a conjecture of Herzog presented in [5], for the edge ideals of square paths and square cycles. 相似文献
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Let I be a homogeneous ideal of a polynomial ring K[x1,…, xn] over a field K, and denote the Castelnuovo–Mumford regularity of I by reg(I). When I is a monomial complete intersection, it is proved that reg(Im) ≤ mreg(I) holds for any m ≥ 1. When n = 3, for any homogeneous ideals I and J of K[x1, x2, x3], one has that reg(I ? J), reg(IJ) and reg(I ∩ J) are all upper bounded by reg(I) +reg(J), while reg(I + J) ≤reg(I) +reg(J) ?1. 相似文献
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We use the correspondence between hypergraphs and their associated edge ideals to study the minimal graded free resolution
of squarefree monomial ideals. The theme of this paper is to understand how the combinatorial structure of a hypergraph ℋ
appears within the resolution of its edge ideal ℐ(ℋ). We discuss when recursive formulas to compute the graded Betti numbers
of ℐ(ℋ) in terms of its sub-hypergraphs can be obtained; these results generalize our previous work (Hà, H.T., Van Tuyl, A.
in J. Algebra 309:405–425, 2007) on the edge ideals of simple graphs. We introduce a class of hypergraphs, which we call properly-connected, that naturally
generalizes simple graphs from the point of view that distances between intersecting edges are “well behaved.” For such a
hypergraph ℋ (and thus, for any simple graph), we give a lower bound for the regularity of ℐ(ℋ) via combinatorial information
describing ℋ and an upper bound for the regularity when ℋ=G is a simple graph. We also introduce triangulated hypergraphs that are properly-connected hypergraphs generalizing chordal
graphs. When ℋ is a triangulated hypergraph, we explicitly compute the regularity of ℐ(ℋ) and show that the graded Betti numbers
of ℐ(ℋ) are independent of the ground field. As a consequence, many known results about the graded Betti numbers of forests
can now be extended to chordal graphs.
Dedicated to Anthony V. Geramita on the occasion of his 65th birthday. 相似文献
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The geometric and algebraic properties of smooth projective varieties with 1-regular structure sheaf are well understood, and the complete classification of these varieties is a classical result. The aim of this paper is to study the next case: smooth projective varieties with 2-regular structure sheaf. First, we give a classification of such varieties using adjunction mappings. Next, under suitable conditions, we study the syzygies of section rings of those varieties to understand the structure of the Betti tables, and show a sharp bound for Castelnuovo–Mumford regularity. 相似文献
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Nursel Erey 《Journal of Pure and Applied Algebra》2019,223(7):3071-3080
Let G be a -free graph with edge ideal . We show that has linear resolution for every . Also, we show that every power of the vertex cover ideal of G has linear quotients. As a result, we describe the Castelnuovo–Mumford regularity of powers of in terms of the maximum degree of G. 相似文献
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Mengyao Sun 《代数通讯》2018,46(11):4830-4843
In this paper, we study the regularity and projective dimension of edge ideals. We provide two upper bounds for the regularity of edge ideals of vertex decomposable graphs in terms of the induced matching number and the number of cycles. Also, we generalize one of the upper bounds given by Dao and Schweig for the projective dimension of hypergraphs. 相似文献
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In 1968, Vizing conjectured that if G is a Δ‐critical graph with n vertices, then α(G)≤n/2, where α(G) is the independence number of G. In this paper, we apply Vizing and Vizing‐like adjacency lemmas to this problem and prove that α(G)<(((5Δ?6)n)/(8Δ?6))<5n/8 if Δ≥6. © 2010 Wiley Periodicals, Inc. J Graph Theory 68: 202‐212, 2011 相似文献
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《代数通讯》2013,41(6):1785-1794
ABSTRACT For projective codimension two surfaces and threefolds whose singular locus is one dimensional, we get the sharp Castelnuovo–Mumford regularity bound in terms of degrees of defining equations and give the classification of nearly extremal cases. This is a generalization of the result of Bertram et al. 相似文献