Upper bounds for the number of facets of a simplicial complex
Authors:
Jürgen Herzog and Takayuki Hibi
Journal:
Proc. Amer. Math. Soc. 125 (1997), 15791583
MSC (1991):
Primary 05D05; Secondary 13D40
MathSciNet review:
1363424
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Abstract: Here we study the maximal dimension of the annihilator ideals of artinian graded rings with a given Hilbert function, where is the polynomial ring in the variables over a field with each , is a graded ideal of , and is the graded maximal ideal of . As an application to combinatorics, we introduce the notion of facets and obtain some informations on the number of facets of simplicial complexes with a given vector.
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 W. Bruns, J. Herzog and U. Vetter, Syzygies and Walks, in ``Commutative Algebra'' (G. Valla, et al., Eds.), World Scientific, 1994, pp. 36  57.
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 G. F. Clements and B. Lindström, A generalization of a combinatorial theorem of Macaulay, J. Combin. Theory 7 (1969), 230  238 MR 40:50
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 C. Greene and D. Kleitman, Proof techniques in the theory of finite sets, in ``Studies in Combinatorics'' (G.C. Rota, ed.), Mathematical Association of America, Washington, D.C., 1978, pp. 22  79. MR 80a:05006
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Additional Information
Jürgen Herzog
Affiliation:
FB 6 Mathematik und Informatik, Universität–GHS–Essen, 45117 Essen, Germany
Email:
mat300@uniessen.de
Takayuki Hibi
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan
Email:
hibi@math.sci.osakau.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993997037040
PII:
S 00029939(97)037040
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
