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| Paper IPM / M / 12783 |
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For a given (d−1)-dimensional simplicial complex Γ, we denote its
h-vector by h(Γ)=(h0(Γ),h1(Γ),…,hd(Γ)) and
set h−1(Γ)=0. The known Swartz equality implies that if ∆
is a (d−1)-dimensional Buchsbaum simplicial complex over a field, then
for every 0 ≤ i ≤ d, the inequality ihi(∆)+ (d−i+1)hi−1(∆) ≥ 0 holds true. In this paper, by using these inequalities, we
give a simple proof for a result of Terai (N. Terai, On h-vectors of
Buchsbaum Stanley-Reisner rings, Hokkaido Math. J. 25 (1996),
no. 1, 137-148) on the h-vectors of Buchsbaum simplicial complexes. We
then generalize the Swartz equality (E. Swartz, Lower bounds for
h-vectors of k-CM, independence, and broken circuit complexes,
SIAM J. Discrete Math. 18 (2004/05), no. 3, 647-661), which in turn
leads to a generalization of the above-mentioned inequalities for
Cohen-Macaulay simplicial complexes in co-dimension t.
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