Survey article: Simplicial complexes satisfying Serre's condition: A survey with some new results

M. R. Pournaki; S. A. Seyed Fakhari; N. Terai; S. Yassemi

doi:10.1216/JCA-2014-6-4-455

Survey article: Simplicial complexes satisfying Serre's condition: A survey with some new results

M. R. Pournaki, S. A. Seyed Fakhari, N. Terai, S. Yassemi

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

The problem of finding a characterization of Cohen-Macaulay simplicial complexes has been studied intensively by many authors. There are several attempts at this problem available for some special classes of simplicial complexes satisfying some technical conditions. This paper is a survey, with some new results, of some of these developments. The new results about simplicial complexes with Serre's condition are an analogue of the known results for Cohen-Macaulay simplicial complexes.

Original language	English
Pages (from-to)	455-483
Number of pages	29
Journal	Journal of Commutative Algebra
Volume	6
Issue number	4
DOIs	https://doi.org/10.1216/JCA-2014-6-4-455
Publication status	Published - 2014
Externally published	Yes

Keywords

(S) simplicial complex
Cohen-Macaulay simplicial complex
Sequentially (S) simplicial complex
Sequentially cohen-macaulay simplicial complex
Simplicial complex

ASJC Scopus subject areas

Algebra and Number Theory

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10.1216/JCA-2014-6-4-455

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title = "Survey article: Simplicial complexes satisfying Serre's condition: A survey with some new results",

abstract = "The problem of finding a characterization of Cohen-Macaulay simplicial complexes has been studied intensively by many authors. There are several attempts at this problem available for some special classes of simplicial complexes satisfying some technical conditions. This paper is a survey, with some new results, of some of these developments. The new results about simplicial complexes with Serre's condition are an analogue of the known results for Cohen-Macaulay simplicial complexes.",

keywords = "(S) simplicial complex, Cohen-Macaulay simplicial complex, Sequentially (S) simplicial complex, Sequentially cohen-macaulay simplicial complex, Simplicial complex",

author = "Pournaki, {M. R.} and {Seyed Fakhari}, {S. A.} and N. Terai and S. Yassemi",

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doi = "10.1216/JCA-2014-6-4-455",

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AU - Terai, N.

AU - Yassemi, S.

PY - 2014

Y1 - 2014

N2 - The problem of finding a characterization of Cohen-Macaulay simplicial complexes has been studied intensively by many authors. There are several attempts at this problem available for some special classes of simplicial complexes satisfying some technical conditions. This paper is a survey, with some new results, of some of these developments. The new results about simplicial complexes with Serre's condition are an analogue of the known results for Cohen-Macaulay simplicial complexes.

AB - The problem of finding a characterization of Cohen-Macaulay simplicial complexes has been studied intensively by many authors. There are several attempts at this problem available for some special classes of simplicial complexes satisfying some technical conditions. This paper is a survey, with some new results, of some of these developments. The new results about simplicial complexes with Serre's condition are an analogue of the known results for Cohen-Macaulay simplicial complexes.

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KW - Cohen-Macaulay simplicial complex

KW - Sequentially (S) simplicial complex

KW - Sequentially cohen-macaulay simplicial complex

KW - Simplicial complex

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Survey article: Simplicial complexes satisfying Serre's condition: A survey with some new results

Abstract

Keywords

ASJC Scopus subject areas

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