On the degree two entry of a Gorenstein h-vector and a conjecture of Stanley
نویسنده
چکیده
In this note 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. In fact, we show that lim r→∞ f(r) r2/3 = 6. In general, we wonder whether our lower bound is sharp for all integers e ≥ 4 and r ≥ 2.
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