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- W2561781206 abstract "The study of the $h$-vectors of graded Gorenstein algebras is an important topic in combinatorial commutative algebra, which despite the large amount of literature produced during the last several years, still presents many interesting open questions. In this note, we commence a study of those unimodal Gorenstein $h$-vectors that do emph{not} satisfy the Stanley-Iarrobino property. Our main results, which are characteristic free, show that such $h$-vectors exist: 1) In socle degree $e$ if and only if $ege 6$; and 2) In every codimension five or greater. The main case that remains open is that of codimension four, where no Gorenstein $h$-vector is known without the Stanley-Iarrobino property. We conclude by proposing the following very general conjecture: The existence of any arbitrary level $h$-vector is emph{independent} of the characteristic of the base field." @default.
- W2561781206 created "2017-01-06" @default.
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- W2561781206 date "2016-12-16" @default.
- W2561781206 modified "2023-09-24" @default.
- W2561781206 title "Unimodal Gorenstein h-vectors without the Stanley-Iarrobino property" @default.
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- W2561781206 doi "https://doi.org/10.48550/arxiv.1612.05522" @default.
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