Upper bounds for the number of facets of a simplicial complex |
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| Authors: | Jü rgen Herzog Takayuki Hibi |
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| Affiliation: | FB 6 Mathematik und Informatik, Universität--GHS--Essen, 45117 Essen, Germany ; Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan |
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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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| Keywords: | |
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