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Stanley's conjecture on the Cohen-Macaulay simplicial complexes of codimension 2 | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 09 مهر 1404 اصل مقاله (344.1 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.34642.5183 | ||
| نویسنده | ||
| Seyed Mohammad Ajdani* | ||
| Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran | ||
| تاریخ دریافت: 14 تیر 1403، تاریخ پذیرش: 07 اسفند 1403 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Stanley depth؛ Cohen-Macaulay؛ partitionable | ||
| مراجع | ||
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