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- W2950654405 abstract "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 $$lim_{rto infty} {f(r)over r^{2/3}}= 6^{2/3}.$$ In general, we wonder whether our lower bound is sharp for all integers $egeq 4$ and $rgeq 2$." @default.
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- W2950654405 date "2006-09-14" @default.
- W2950654405 modified "2023-09-27" @default.
- W2950654405 title "On the degree two entry of a Gorenstein $h$-vector and a conjecture of Stanley" @default.
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