Ideals Whose First Two Betti Numbers Are Close

Optimal 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.

BETTI NUMBERS FOR p STABLE IDEALS

Betti numbers of mixed product ideals

We compute the Betti numbers of the resolution of a special class of square-free monomial ideals, the ideals of mixed products. Moreover when these ideals are Cohen-Macaulay we calculate their type. Mathematics Subject Classification (2000). Primary 13P10; Secondary 13B25.

Minimal Graded Betti Numbers and Stable Ideals

Let k be a field, and let R = k[x1, x2, x3]. Given a Hilbert function H for a cyclic module over R, we give an algorithm to produce a stable ideal I such that R/I has Hilbert function H and uniquely minimal graded Betti numbers among all R/J with the same Hilbert function, where J is another stable ideal in R. We also show that such an algorithm is impossible in more variables and disprove a re...

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...