On the Betti Numbers of Shifted Complexes of Stable Simplicial Complexes

Details On the Betti Numbers of Shifted Complexes of Stable Simplicial Complexes On the Betti Numbers of Shifted Complexes of Stable Simplicial Complexes

2004-11-20

arxiv.org/abs/math/0411449v1

Mathematics

Commutative Algebra

9 pages

Scientific paper

Let $\Delta$ be a stable simplicial complex on $n$ vertexes. Over an arbitrary base field $K$, the symmetric algebraic shifted complex $\Delta^s$ of $\Delta$ is defined. It is proved that the Betti numbers of the Stanley-Reisner ideals in the polynomial ring $K[x_1,x_2,...,x_n]$ of the symmetric algebraic shifted, exterior algebraic shifted and combinatorial shifted complexes of $\Delta$ are equal.

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