Satoshi Murai

Regularity bounds for binomial edge ideals

We show that the Castelnuovo-Mumford regularity of the binomial edge ideal of a graph is bounded below by the length of its longest induced path and bounded above by the number of its vertices.

On r-stacked triangulated manifolds

The notion of r-stackedness for simplicial polytopes was introduced by McMullen and Walkup in 1971 as a generalization of stacked polytopes. In this paper, we define the r-stackedness for triangulated homology manifolds and study its basic properties. In addition, we find a new necessary condition for face vectors of triangulated manifolds when all the vertex links are polytopal.

Algebraic shifting of strongly edge decomposable spheres

Recently, Nevo introduced the notion of strongly edge decomposable spheres. In this paper, we characterize algebraic shifted complexes of those spheres. Algebraically, this result yields the characterization of the generic initial ideal of the Stanley-Reisner ideal of Gorenstein^* complexes having the strong Lefschetz property in characteristic 0.

THE DEPTH OF AN IDEAL WITH A GIVEN HILBERT FUNCTION

Let A = K[x 1 ,...,x n ] denote the polynomial ring in n variables over a field K with each deg x i = 1. Let I be a homogeneous ideal of A with I ≠A and H A/I the Hilbert function of the quotient algebra A/I. Given a numerical function H: N → N satisfying H = H A/I for some homogeneous ideal I of A, we write A H for the set of those integers 0 ≤ r < n such that there exists a homogeneous ideal I of A with H A / I = H and with depth A/I = r. It will be proved that one has either A H = {0,1,...,b} for some 0 ≤ b < n or |AH| = 1.

Kruskal-Katona type theorems for clique complexes arising from chordal and strongly chordal graphs

A forest is the clique complex of a strongly chordal graph and a quasi-forest is the clique complex of a chordal graph. Kruskal-Katona type theorems for forests, quasi-forests, pure forests and pure quasi-forests will be presented.

Face vectors of simplicial cell decompositions of manifolds

In this paper, we study face vectors of simplicial posets that are the face posets of cell decompositions of topological manifolds without boundary. We characterize all possible face vectors of simplicial posets whose geometric realizations are homeomorphic to the product of spheres. As a corollary, we obtain the characterization of face vectors of simplicial posets whose geometric realizations are odd-dimensional manifolds without boundary.

INVARIANCE OF PONTRJAGIN CLASSES FOR BOTT MANIFOLDS

A Bott manifold is the total space of some iterated

Algebraic shifting and graded Betti numbers

\mathbb C P^1

Algebraic shifting of cyclic polytopes and stacked polytopes

-bundle over a point. We prove that any graded ring isomorphism between the cohomology rings of two Bott manifolds preserves their Pontrjagin classes. Moreover, we prove that such an isomorphism is induced from a diffeomorphism if the Bott manifolds are

Balanced generalized lower bound inequality for simplicial polytopes

\mathbb Z/2