منابع مشابه
Betti numbers of transversal monomial ideals
In this paper, by a modification of a previously constructed minimal free resolution for a transversal monomial ideal, the Betti numbers of this ideal is explicitly computed. For convenient characteristics of the ground field, up to a change of coordinates, the ideal of t-minors of a generic pluri-circulant matrix is a transversal monomial ideal . Using a Gröbner basis for this ideal, it is sho...
متن کاملBetti Numbers of Monomial Ideals and Shifted Skew Shapes
We present two new problems on lower bounds for Betti numbers of the minimal free resolution for monomial ideals generated in a fixed degree. The first concerns any such ideal and bounds the total Betti numbers, while the second concerns ideals that are quadratic and bihomogeneous with respect to two variable sets, but gives a more finely graded lower bound. These problems are solved for certai...
متن کاملExtremal Betti Numbers and Applications to Monomial Ideals
Recall that the (Mumford-Castelnuovo) regularity of M is the least integer ρ such that for each i all free generators of Fi lie in degree ≤ i + ρ, that is βi,j = 0, for j > i + ρ. In terms of Macaulay [Mac] regularity is the number of rows in the diagram produced by the “betti” command. A Betti number βi,j 6= 0 will be called extremal if βl,r = 0 for all l ≥ i and r ≥ j + 1, that is if βi,j is ...
متن کاملMonomial ideals , edge ideals of hypergraphs , and their graded Betti numbers
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...
متن کاملLyubeznik Numbers of Monomial Ideals
Let R = k[x1, ..., xn] be the polynomial ring in n independent variables, where k is a field. In this work we will study Bass numbers of local cohomology modules H I (R) supported on a squarefree monomial ideal I ⊆ R. Among them we are mainly interested in Lyubeznik numbers. We build a dictionary between the modules H I (R) and the minimal free resolution of the Alexander dual ideal I∨ that all...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07557-4