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Open AccessArticle

Cohen-Macaulay and (S2) Properties of the Second Power of Squarefree Monomial Ideals

by Do Trong Hoang 1,†, Giancarlo Rinaldo 2,† and Naoki Terai 3,*,†
Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam
Department of Mathematics, University of Trento, via Sommarive, 14, 38123 Povo (Trento), Italy
Faculty of Education, Saga University, Saga 840-8502, Japan
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(8), 684;
Received: 16 June 2019 / Revised: 29 July 2019 / Accepted: 30 July 2019 / Published: 31 July 2019
(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)
We show that Cohen-Macaulay and (S 2 ) properties are equivalent for the second power of an edge ideal. We give an example of a Gorenstein squarefree monomial ideal I such that S / I 2 satisfies the Serre condition (S 2 ), but is not Cohen-Macaulay. View Full-Text
Keywords: Stanley-Reisner ideal; edge ideal; Cohen-Macaulay; (S2) condition Stanley-Reisner ideal; edge ideal; Cohen-Macaulay; (S2) condition
MDPI and ACS Style

Hoang, D.T.; Rinaldo, G.; Terai, N. Cohen-Macaulay and (S2) Properties of the Second Power of Squarefree Monomial Ideals. Mathematics 2019, 7, 684.

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