Naoki Terai

Computation of betti numbers of monomial ideals associated with cyclic polytopes

We give a combinatorial formula for the Betti numbers which appear in a minimal free resolution of the Stanley-Reisner ringk[Δ(P)]=A/IΔ(P) of the boundary complex Δ(P) of an odd-dimensional cyclic polytopePover a fieldk. A corollary to the formula is that the Betti number sequence ofk[Δ(P)] is unimodal and does not depend on the base fieldk.

Cohen-Macaulay edge ideal whose height is half of the number of vertices

We consider a class of graphs

Computation of betti numbers of monomial ideals associated with stacked polytopes

G

On the second powers of Stanley-Reisner ideals

such that the height of the edge ideal

Arithmetical Ranks of Stanley–Reisner Ideals of Simplicial Complexes with a Cone

I(G)

The Stanley–Reisner Ideals of Polygons as Set-Theoretic Complete Intersections

is half of the number

Buchsbaum Stanley–Reisner rings with minimal multiplicity

\sharp V(G)

Finite Free Resolutions and 1-Skeletonsof Simplicial Complexes

of the vertices. We give Cohen-Macaulay criteria for such graphs.

Arithmetical Rank of Squarefree Monomial Ideals Generated by Five Elements or with Arithmetic Degree Four

LetP(v, d) be a stackedd-polytope withv vertices, δ(P(v, d)) the boundary complex ofP(v, d), andk[Δ(P(v, d))] =A/IΔ(P(v,d)) the Stanley-Reisner ring of Δ(P(v,d)) over a fieldk. We compute the Betti numbers which appear in a minimal free resolution ofk[Δ(P(v,d))] overA, and show that every Betti number depends only onv andd and is independent of the base fieldk. We also show that the Betti number sequences above are unimodal.

Sequentially

In this paper, we study several properties of the second power