Hilbert series and suspensions of graphs

We explore the relationship between the Hilbert series of the edge ideal I of a graph and the combinatorial invariants of the graph, with a focus on identifying relationships between entries of the h -vector of R / I and graph properties. When the graph is a suspension, and thus Cohen–Macaulay with...

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Bibliographic Details
Published inSão Paulo Journal of Mathematical Sciences Vol. 17; no. 1; pp. 17 - 35
Main Authors Brennan, Joseph, Morey, Susan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2023
Springer Nature B.V
Subjects
Apexes
Combinatorial analysis
Graph theory
Mathematics
Mathematics and Statistics
Special Issue in Honor of Rafael H. Villarreal on the Occasion of His 70th Birthday
05E40
13D40
Hilbert functions
Hilbert series
Edge ideals
Monomial ideals
13F55
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Summary:We explore the relationship between the Hilbert series of the edge ideal I of a graph and the combinatorial invariants of the graph, with a focus on identifying relationships between entries of the h -vector of R / I and graph properties. When the graph is a suspension, and thus Cohen–Macaulay with positive entries in the h -vector, we show that those entries are equal to the entries of the f -vector of the Stanley–Reisner complex of the induced subgraph on the vertices of degree at least 2.
ISSN:1982-6907
2316-9028
2306-9028
DOI:10.1007/s40863-022-00329-5