منابع مشابه
Extremal Betti Numbers of Some Classes of Binomial Edge Ideals
Let G be a simple graph on the vertex set [n] with edge set E(G) and let S be the polynomial ring K[x1, . . . , xn, y1, . . . , yn] in 2n variables endowed with the lexicographic order induced by x1 > · · · > xn > y1 > · · · > yn. The binomial edge ideal JG ⊂ S associated with G is generated by all the binomials fij = xiyj−xjyi with {i, j} ∈ E(G). The binomial edge ideals were introduced in [5]...
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...
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Upper bounds on the topological Betti numbers of Vietoris-Rips complexes are established, and examples of such complexes with high Betti
متن کاملOptimal Betti Numbers of Forest Ideals
We prove a tight lower bound on the algebraic Betti numbers of tree and forest ideals and an upper bound on certain graded Betti numbers of squarefree monomial ideals.
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2019
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-019-01322-9