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

Authors

Juan Migliore, University of Notre Dame
Uwe Nagel, University of Kentucky
Fabrizio Zanello, Michigan Technological UniversityFollow

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

Recommended Citation

Migliore, J., Nagel, U., & Zanello, F. (2008). On the degree two entry of a Gorenstein h-vector and a conjecture of Stanley. Proceedings of the American Mathematical Society, 136, 2755-2762. http://doi.org/10.1090/S0002-9939-08-09456-2
Retrieved from: https://digitalcommons.mtu.edu/math-fp/43