We give criteria for graded ideals to have the property that all their powers are componentwise linear. Typical examples to which our criteria can be applied include the vertex cover ideals ofâ€¦ (More)

We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals areâ€¦ (More)

A compressed polytope is an integral convex polytope any of whose reverse lexicographic initial ideals is squarefree. A sufficient condition for a (0, 1)-polytope to be compressed will be presented.â€¦ (More)

Let f(d) = (fs, fi, . . . . fd,) be the f-vector of a Cohen-Macaulay complex A. Bjijrner proved that (*) fief++, for any O<ii[d/2] and (**) f0 Q fi < < fr+ i rP1. Recently, Stanley generalizedâ€¦ (More)

The aim of this paper is to characterize simplicial complexes which have standard graded vertex cover algebras. This property has several nice consequences for the squarefree monomial ideals definingâ€¦ (More)

Athanasiadis [Ehrhart polynomials, simplicial polytopes, magic squares and a conjecture of Stanley, J. Reine Angew. Math., to appear.] studies an effective technique to show that Gorenstein sequencesâ€¦ (More)

Several polytopes arise from finite graphs. For edge and symmetric edge polytopes, in particular, exhaustive computation of the Ehrhart polynomials not merely supports the conjecture of Beck et al.â€¦ (More)

1.1. Let V = {x1, x2, . . . , xv} be a finite set, called the vertex set , and1 a simplicial complexon V . Thus1 is a collection of subsets of V such that (i){xi } âˆˆ 1 for every 1 â‰¤ i â‰¤ v and (ii)Ïƒ âˆˆâ€¦ (More)

In this paper we introduce a new and large family of configurations whose toric ideals possess quadratic GrÃ¶bner bases. As an application, a generalization of algebras of Segreâ€“Veronese type will beâ€¦ (More)