@article{1920b033fed54990880e97cebbe2f379,
title = "Cohen-Macaulay and (S2) properties of the second power of squarefree monomial ideals",
abstract = "We show that Cohen-Macaulay and (S2) 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/I2 satisfies the Serre condition (S2), but is not Cohen-Macaulay.",
keywords = "(S) condition, Cohen-Macaulay, Edge ideal, Stanley-Reisner ideal",
author = "Hoang, {Do Trong} and Giancarlo Rinaldo and Naoki Terai",
note = "Funding Information: Funding: This work was partially supported by a JSPS Grant-in Aid for Scientific Research (C) 18K03244. The research of Do Trong Hoang was supported by the project ICRTM01 2019.02 of the International Center for Research and Postgraduate Training in Mathematics, VAST. Publisher Copyright: {\textcopyright} 2019 by the authors.",
year = "2019",
doi = "10.3390/math7080684",
language = "English",
volume = "7",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "8",
}