Sách A combinatorial proof of a formula for Betti numbers of a stacked polytope

Abstract
For a simplicial complex ∆, the graded Betti number βi,j (k[∆]) of the Stanley-
Reisner ring k[∆] over a field k has a combinatorial interpretation due to Hochster.
Terai and Hibi showed that if ∆ is the boundary complex of a d-dimensional stacked
polytope with n vertices for d > 3, then βkư 1,k(k[∆]) = (k ư 1)