Geodesic
Bounds for the regularity of product of edge ideals
Banerjee, Arindam1 ; Das, Priya2 ; Selvaraja, S3
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
Algebraic Combinatorics, Tome 5 (2022) no. 5, pp. 1015-1032 Cet article a éte moissonné depuis la source Numdam

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Let I and J be edge ideals in a polynomial ring R=𝕂[x 1 ,...,x n ] with I⊆J. In this paper, we obtain a general upper and lower bound for the Castelnuovo–Mumford 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 ⋯J d , d∈{3,4}, where J 1 ,...,J d are edge ideals, J 1 ⊆J 2 ⊆⋯⊆J 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–Mumford 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Bounds for the regularity of product of edge ideals},
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     pages = {1015--1032},
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Banerjee, Arindam; Das, Priya; Selvaraja, S. Bounds for the regularity of product of edge ideals. Algebraic Combinatorics, Tome 5 (2022) no. 5, pp. 1015-1032. doi: 10.5802/alco.234

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