Regularity of powers of squarefree monomial ideals

Banerjee, Arindam; Chakraborty, Bidwan; Das, Kanoy Kumar; Mandal, Mousumi; Selvaraja, S.

doi:10.1016/j.jpaa.2021.106807

Cited by 3 publications

(1 citation statement)

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“…It is an open problem whether v(I) ≤ reg(S/I) + 1 holds for any squarefree monomial ideal. Upper and lower bounds for the regularity of edge ideals and their powers were given in [6][7][8][9][10][11][12][13][14][15]; see Section 2. Using the polarization technique of Fröberg [16], we give an upper bound for the regularity of a monomial ideal I in terms of the dimension of S/I and the exponents of the monomials that generate I (Proposition 2).…”

Section: Introductionmentioning

confidence: 99%

Induced Matchings and the v-Number of Graded Ideals

2021

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We give a formula for the v-number of a graded ideal that can be used to compute this number. Then, we show that for the edge ideal I(G) of a graph G, the induced matching number of G is an upper bound for the v-number of I(G) when G is very well-covered, or G has a simplicial partition, or G is well-covered connected and contains neither four, nor five cycles. In all these cases, the v-number of I(G) is a lower bound for the regularity of the edge ring of G. We classify when the induced matching number of G is an upper bound for the v-number of I(G) when G is a cycle and classify when all vertices of a graph are shedding vertices to gain insight into the family of W2-graphs.

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