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On the Betti Numbers of Shifted Complexes of Stable Simplicial Complexes

Zhongming Tang·Guifen Zhuang
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Abstract

Let $Δ$ be a stable simplicial complex on $n$ vertexes. Over an arbitrary base field $K$, the symmetric algebraic shifted complex $Δ^s$ of $Δ$ 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 $Δ$ are equal.

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Zhongming Tang, Guifen Zhuang. 2004-11-20. On the Betti Numbers of Shifted Complexes of Stable Simplicial Complexes. https://arxiv.org/abs/math/0411449

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