In prime characteristic there are important invariants that allow us to measure singularities. For certain cases, it is known they rational numbers. this article, we show property for Stanley-Reisner rings in several cases.

For t in Nn, E.Miller has defined a category of t-determined modules over the polynomial ring S in n variables. We consider the Auslander-Reiten translate, Nt, on the (derived) category of such modules. A monomial ideal I is t-determined if every generator x has a ≤ t. We compute the multigraded cohomologyand betti spaces of N k t (S/I) for every iterate k, and also the Smodule structure of the...

We determine a term order on the monomials in the variables Xij , 1 ≤ i < j ≤ n, such that corresponding initial ideal of the ideal of Pfaffians of degree r of a generic n by n skew-symmetric matrix is the Stanley-Reisner ideal of a join of a simplicial sphere and a simplex. Moreover, we demonstrate that the Pfaffians of the 2r by 2r skew-symmetric submatrices form a Gröbner basis for the given...

We study a natural generalization of the noncrossing relation between pairs of elements in [n] to k-tuples in [n]. We show that the flag simplicial complex on ( [n] k ) induced by this relation is a regular, unimodular and flag triangulation of the order polytope of the poset given by the product [k]× [n− k] of two chains, and it is the join of a simplex and a sphere (that is, it is a Gorenstei...

We recall numerical criteria for Cohen–Macaulayness related to system of parameters and introduce monomial ideals König type which include the edge graphs. show that a ideal is if only its corresponding residue class ring admits whose elements are form $$x_i-x_j$$ . This provides an algebraic characterization use this special parameter systems study graphs order complex certain family posets. F...

This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective dimension of these ideals, which turns out to be a new numerical invariant of forests. Finally, we propose a possible extension of this invariant to general graphs. 0. Introduction Throughout this pape...

We determine the simplicial complexes ∆ whose Stanley-Reisner ideals I∆ have the following property: for all n ≥ 1 the powers In ∆ have linear resolutions and finite length local cohomologies.