Stanley’s nonunimodal Gorenstein $h$-vector is optimal

Autor:	Fabrizio Zanello, Juan C. Migliore
Rok vydání:	2016
Předmět:	Hilbert series and Hilbert polynomial Sequence Mathematics::Commutative Algebra Degree (graph theory) Applied Mathematics General Mathematics Mathematics::Rings and Algebras Codimension h-vector Unimodality Socle Combinatorics symbols.namesake symbols Mathematics
Zdroj:	Proceedings of the American Mathematical Society. 145:1-9
ISSN:	1088-6826 0002-9939
DOI:	10.1090/proc/13381
Popis:	We classify all possible $h$-vectors of graded artinian Gorenstein algebras in socle degree 4 and codimension $\leq 17$, and in socle degree 5 and codimension $\leq 25$. We obtain as a consequence that the least number of variables allowing the existence of a nonunimodal Gorenstein $h$-vector is 13 for socle degree 4, and 17 for socle degree 5. In particular, the smallest nonunimodal Gorenstein $h$-vector is $(1,13,12,13,1)$, which was constructed by Stanley in his 1978 seminal paper on level algebras. This solves a long-standing open question in this area. All of our results are characteristic free.
Databáze:	OpenAIRE
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