“School of Mathematics”
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| Paper IPM / M / 11812 |
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| Abstract: | |||||
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Let ∆ be a (d−1)-dimensional simplicial complex and let h(∆) = (h0,h1,…,hd) be its h-vector. A recent result of Murai and
Terai guarantees that if ∆ satisfies Serre's condition (Sr), then
(h0,h1,…,hr) is an M-vector and hr+hr+1+…+hd is
nonnegative. In this article, we extend the result of Murai and Terai by
giving r extra necessary conditions. More precisely, we prove that if
∆ satisfies Serre's condition (Sr), then ((i) || (i))hr+((i+1) || (i))hr+1+…+((i+d−r) || (i))hd, 0 ≤ i ≤ r ≤ d, are
all nonnegative.
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