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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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[1] M. Barile and N. Terai, Arithmetical ranks of Stanley-Reisner ideals of simplicial complexes with a cone, Comm. Algebra 38 (2010), no. 10, 3686-3698. [2] A Conca and E. De Negri, M-sequences, graph ideals and ladder ideals of linear type, J. Algebra 211 (1999), no. 2, 599-624. [3] J. Eagon and V. Reiner, Resolutions of Stanley-Reisner rings and Alexander duality, J. Pure Appl. Algebra 130 (1998), 265-275. [4] J. Herzog and T. Hibi, Componentwise linear ideals, Nagoya Math. J. 153 (1999), 141-153. [5] J. Herzog, A. Soleyman Jahan, and S. Yassemi, Stanley decompositions and partitionable simplicial complexes, J. Algebr. Comb. 27 (2008), 113-125. [6] M. Miyazaki, *On 2-Buchsbaum Complexes*, J. Math. Kyoto Univ. 30 (1990), 367-392. [7] R. Rahmati-Asghar and S. Yassemi, k-decomposable monomial ideals, Algebra Colloq. 22 (2015), Special Issue no. 1, 745-756. [8] R.P. Stanley, Linear Diophantine Equations and Local Cohomology, Invent. Math. 68 (1982), 175-193. [9] R.P. Stanley, Combinatorics and Commutative Algebra, Second edition. Progress in Mathematics 41, Birkhauser Boston, 1996. [10] R.P. Stanley, Positivity problems and conjectures in algebraic combinatorics, Mathematics: Frontiers and perspectives, Amer. Math. Soc., Providence, RI, 2000, pp. 295-319. [11] X. Zheng, Homological properties of monomial ideals associated to quasi-trees and lattices, Ph.D Thesis, University of Essen, 2004. | ||
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