Title

On the degree two entry of a Gorenstein h-vector and a conjecture of Stanley

Document Type

Article

Publication Date

4-10-2008

Abstract

In this short paper we establish a (non-trivial) lower bound on the

degree two entry h2 of a Gorenstein h-vector of any given socle degree e and

any codimension r.

In particular, when e = 4, that is, for Gorenstein h-vectors of the form

h = (1, r,h2, r, 1), our lower bound allows us to prove a conjecture of Stanley

on the order of magnitude of the minimum value, say f(r), that h2 may assume.

Publisher's Statement

Copyright 2008 American Mathematical Society. Publisher’s version of record: https://doi.org/10.1090/S0002-9939-08-09456-2

Publication Title

Proceedings of the American Mathematical Society

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