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Open AccessArticle

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

by 1,†, Giancarlo Rinaldo 2,† and Naoki Terai 3,*,†
1
Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam
2
Department of Mathematics, University of Trento, via Sommarive, 14, 38123 Povo (Trento), Italy
3
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; https://doi.org/10.3390/math7080684
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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