@article{e2f8341cd25f4c8abf24bd7a5dcd636d,
title = "SIMPLICIAL COMPLEXES SATISFYING SERRE{\textquoteright}S CONDITION VERSUS THE ONES WHICH ARE COHEN–MACAULAY IN A FIXED CODIMENSION",
abstract = "In this paper, we give necessary and sufficient conditions for a simplicial complex with small codimension to satisfy the Serre{\textquoteright}s condition (Sr) as well as the CMt property. We also give a connection between being (Sr) and being CMt. The main tools for this study are local cohomology modules and their Matlis duals.",
keywords = "(Sr) simplicial complex, CMt simplicial complex, Cohen–Macaulay ring, Cohen–Macaulay simplicial complex, simplicial complex",
author = "Pournaki, {M. R.} and M. Poursoltani and N. Terai and S. Yassemi",
note = "Funding Information: ∗Received by the editors August 9, 2021; accepted for publication (in revised form) June 16, 2022; published electronically October 19, 2022. https://doi.org/10.1137/21M1439687 Funding: The research of the first author was in part supported by a grant from the World Academy of Sciences (TWAS-UNESCO Associateship), 3240295905. The research of the third author was in part supported by a grant from the Japan Society for the Promotion of Science (JSPS Grant-in-Aid for Scientific Research (C)), 18K03244. †Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11155-9415, Tehran, Iran (pournaki@ipm.ir, mpoursoltaniz@gmail.com). ‡Department of Mathematics, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530, Japan (terai@okayama-u.ac.jp). §School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran (yassemi@ut.ac.ir). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",
year = "2022",
doi = "10.1137/21M1439687",
language = "English",
volume = "36",
pages = "2506--2522",
journal = "SIAM Journal on Discrete Mathematics",
issn = "0895-4801",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}