Satoshi Murai
Osaka University
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Publication
Featured researches published by Satoshi Murai.
Journal of Commutative Algebra | 2013
Kazunori Matsuda; Satoshi Murai
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.
Journal of Algebraic Combinatorics | 2014
Satoshi Murai; Eran Nevo
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.
Journal of Combinatorial Theory | 2010
Satoshi Murai
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.
arXiv: Commutative Algebra | 2008
Satoshi Murai; Takayuki Hibi
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.
Combinatorica | 2008
Jürgen Herzog; Satoshi Murai; Xinxian Zheng; Takayuki Hibi; Ngo Viet Trung
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.
Israel Journal of Mathematics | 2013
Satoshi Murai
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.
Algebraic & Geometric Topology | 2015
Suyoung Choi; Mikiya Masuda; Satoshi Murai
A Bott manifold is the total space of some iterated
Transactions of the American Mathematical Society | 2008
Satoshi Murai; Takayuki Hibi
\mathbb C P^1
Discrete Mathematics | 2007
Satoshi Murai
-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
Selecta Mathematica-new Series | 2018
Martina Juhnke-Kubitzke; Satoshi Murai
\mathbb Z/2