Computation of Betti numbers of monomial ideals associated with cyclic polytopes

N. Terai; T. Hibi

doi:10.1007/BF02711496

Computation of Betti numbers of monomial ideals associated with cyclic polytopes

N. Terai, T. Hibi

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We give a combinatorial formula for the Betti numbers which appear in a minimal free resolution of the Stanley-Reisner ring k[Δ(P)] = A/I_Δ(P), of the boundary complex Δ(P) of an odd-dimensional cyclic polytope P over a field k. A corollary to the formula is that the Betti number sequence of k[Δ(P)] is unimodal and does not depend on the base field k.

Original language	English
Pages (from-to)	287-295
Number of pages	9
Journal	Discrete and Computational Geometry
Volume	15
Issue number	3
DOIs	https://doi.org/10.1007/BF02711496
Publication status	Published - Apr 1996
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/BF02711496

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abstract = "We give a combinatorial formula for the Betti numbers which appear in a minimal free resolution of the Stanley-Reisner ring k[Δ(P)] = A/IΔ(P), of the boundary complex Δ(P) of an odd-dimensional cyclic polytope P over a field k. A corollary to the formula is that the Betti number sequence of k[Δ(P)] is unimodal and does not depend on the base field k.",

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AB - We give a combinatorial formula for the Betti numbers which appear in a minimal free resolution of the Stanley-Reisner ring k[Δ(P)] = A/IΔ(P), of the boundary complex Δ(P) of an odd-dimensional cyclic polytope P over a field k. A corollary to the formula is that the Betti number sequence of k[Δ(P)] is unimodal and does not depend on the base field k.

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ER -

Computation of Betti numbers of monomial ideals associated with cyclic polytopes

Abstract

ASJC Scopus subject areas

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