TY - JOUR
T1 - Computation of Betti numbers of monomial ideals associated with stacked polytopes
AU - Terai, Naoki
AU - Hibi, Takayuki
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 1997/4
Y1 - 1997/4
N2 - Let P(v, d) be a stacked d-polytope with v vertices, Δ(P(v,d)) the boundary complex of P(v,d), and k[Δ(P(v,d))] = A/IΔ(P(v,d)) the Stanley-Reisner ring of Δ(P(v,d)) over a field k. We compute the Betti numbers which appear in a minimal free resolution of k[Δ(P(v,d))] over A, and show that every Betti number depends only on v and d and is independent of the base field k. We also show that the Betti number sequences above are unimodal.
AB - Let P(v, d) be a stacked d-polytope with v vertices, Δ(P(v,d)) the boundary complex of P(v,d), and k[Δ(P(v,d))] = A/IΔ(P(v,d)) the Stanley-Reisner ring of Δ(P(v,d)) over a field k. We compute the Betti numbers which appear in a minimal free resolution of k[Δ(P(v,d))] over A, and show that every Betti number depends only on v and d and is independent of the base field k. We also show that the Betti number sequences above are unimodal.
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U2 - 10.1007/bf02678204
DO - 10.1007/bf02678204
M3 - Article
AN - SCOPUS:0031116507
SN - 0025-2611
VL - 92
SP - 447
EP - 453
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 4
ER -