×

The Hilbert series of the clique complex. (English) Zbl 1095.13022

Summary: For a graph \(G\), we show a theorem that establishes a correspondence between the fine Hilbert series of the Stanley-Reisner ring of the clique complex for the complementary graph of \(G\) and the fine subgraph polynomial of \(G\). We obtain from this theorem some corollaries regarding the independent set complex and the matching complex.

MSC:

13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
05E99 Algebraic combinatorics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Renteln, P., The Hilbert series of the Face Ring of a Flag Complex, Graphs and Combinatorics, 18, 3, 605-619 (2002) · Zbl 1031.13012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.