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Upper bounds for the number of facets
of a simplicial complex

Authors: Jürgen Herzog and Takayuki Hibi
Journal: Proc. Amer. Math. Soc. 125 (1997), 1579-1583
MSC (1991): Primary 05D05; Secondary 13D40
MathSciNet review: 1363424
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Abstract | References | Similar Articles | Additional Information

Abstract: Here we study the maximal dimension of the annihilator ideals
$0:_{A}m^{j}$ of artinian graded rings $A = P / (I, x_1^2, x_2^2, \ldots , x_v^2)$ with a given Hilbert function, where $P$ is the polynomial ring in the variables $x_1, x_2, \ldots , x_v$ over a field $K$ with each $\deg x_i = 1$, $I$ is a graded ideal of $P$, and $m$ is the graded maximal ideal of $A$. As an application to combinatorics, we introduce the notion of $j$-facets and obtain some informations on the number of $j$-facets of simplicial complexes with a given $f$-vector.

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Additional Information

Jürgen Herzog
Affiliation: FB 6 Mathematik und Informatik, Universität–GHS–Essen, 45117 Essen, Germany

Takayuki Hibi
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan

Received by editor(s): August 28, 1995
Received by editor(s) in revised form: October 26, 1995
Additional Notes: This paper was written while the authors were staying at the Mathematische Forschungsinstitut Oberwolfach in the frame of the RiP program which is financed by Volkswagen–Stiftung
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1997 American Mathematical Society