On the Betti Numbers of Shifted Complexes of Stable Simplicial Complexes

Zhongming Tang; Guifen Zhuang

On the Betti Numbers of Shifted Complexes of Stable Simplicial Complexes

Commutative Algebra 2007-05-23 v1

Authors: Zhongming Tang , Guifen Zhuang

Abstract

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.

Keywords

stable simplicial complex shifted complex betti numbers stanley-reisner ideal symmetric algebraic shifted complex

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@article{arxiv.math/0411449,
  title  = {On the Betti Numbers of Shifted Complexes of Stable Simplicial Complexes},
  author = {Zhongming Tang and Guifen Zhuang},
  journal= {arXiv preprint arXiv:math/0411449},
  year   = {2007}
}

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9 pages

On the Betti Numbers of Shifted Complexes of Stable Simplicial Complexes

Abstract

Keywords

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