Bounds for the regularity of product of edge ideals
Algebraic Combinatorics, Volume 5 (2022) no. 5, pp. 1015-1032.

Let I and J be edge ideals in a polynomial ring R=ūĚēā[x 1 ,...,x n ] with I‚äÜJ. In this paper, we obtain a general upper and lower bound for the Castelnuovo‚ÄďMumford regularity of IJ in terms of certain invariants associated with I and J. Using these results, we explicitly compute the regularity of IJ for several classes of edge ideals. In particular, we compute the regularity of IJ when J has a linear resolution. Finally, we compute the precise expression for the regularity of J 1 J 2 ‚čĮJ d , d‚ąą{3,4}, where J 1 ,...,J d are edge ideals, J 1 ‚äÜJ 2 ‚äÜ‚čĮ‚äÜJ d and J d is the edge ideal of a complete graph.

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DOI: 10.5802/alco.234
Classification: 13D02,  05E45,  05C70
Keywords: Castelnuovo‚ÄďMumford regularity, product of edge ideals, linear resolution
Banerjee, Arindam 1; Das, Priya 2; Selvaraja, S 3

1 Department of Mathematics Indian Institute of Technology Kharagpur 721302 India
2 Department of Mathematics National Institute of Technology Calicut Kerala 673601 India
3 Chennai Mathematical Institute H1 SIPCOT IT Park Siruseri Kelambakkam Chennai India 603103
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Banerjee, Arindam; Das, Priya; Selvaraja, S. Bounds for the regularity of product of edge ideals. Algebraic Combinatorics, Volume 5 (2022) no. 5, pp. 1015-1032. doi : 10.5802/alco.234. https://alco.centre-mersenne.org/articles/10.5802/alco.234/

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