A Combinatorial Proof of a Formula for Betti Numbers of a Stacked Polytope
نویسندگان
چکیده
For a simplicial complex ∆, the graded Betti number βi,j(k[∆]) of the StanleyReisner 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 βk−1,k(k[∆]) = (k − 1) ` n−d k ́ . We prove this combinatorially.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 17 شماره
صفحات -
تاریخ انتشار 2010