On the degree two entry of a Gorenstein $h$-vector and a conjecture of Stanley
| dc.creator | Migliore, Juan C. | |
| dc.creator | Nagel, Uwe | |
| dc.creator | Zanello, Fabrizio | |
| dc.date | 2006-09-14 | |
| dc.date | 2007-11-27 | |
| dc.date.accessioned | 2026-07-07T12:50:39Z | |
| dc.date.available | 2026-07-07T12:50:39Z | |
| dc.description | In this note we establish a (non-trivial) lower bound on the degree two entry $h_2$ 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 $h=(1,r,h_2,r,1)$, our lower bound allows us to prove a conjecture of Stanley on the order of magnitude of the minimum value, say $f(r)$, that $h_2$ may assume. In fact, we show that $$\lim_{r\to \infty} {f(r)\over r^{2/3}}= 6^{2/3}.$$ In general, we wonder whether our lower bound is sharp for all integers $e\geq 4$ and $r\geq 2$. | |
| dc.description | A few minor changes. To appear in Proc. of the AMS | |
| dc.identifier | https://arxiv.org/abs/math/0609414 | |
| dc.identifier | http://arxiv.org/abs/math/0609414 | |
| dc.identifier | Proc. Amer. Math. Soc. 136 (2008), No. 8, 2755-2762 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222744 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 13E10 (Primary); 13H10, 13D40 (Secondary) | |
| dc.title | On the degree two entry of a Gorenstein $h$-vector and a conjecture of Stanley | |
| dc.type | text |