International Journal of Nonlinear Analysis and Applications

Stanley's conjecture on the Cohen-Macaulay simplicial complexes of codimension 2

Articles in Press

Document Type : Research Paper

Author

Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran

Abstract

Let $\Delta$ be a simplicial complex on vertex set $\{ x_{1}, \ldots, x_{n} \}$. It is shown that if $\Delta$ is a Cohen-Macaulay simplicial complex of codimension 2, then $\Delta$ is partitionable and Stanley's conjecture holds for $K[\Delta]$. As a consequence, we show that if $\Delta$ is a quasi-forest simplicial complex, then $\Delta^\vee$ is shellable.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 01 October 2025
  • Receive Date: 04 July 2024
  • Accept Date: 25 February 2025