Rees algebras of filtrations of covering polyhedra and integral closure of powers of monomial ideals

Grisalde, Gonzalo; Seceleanu, Alexandra; Villarreal, Rafael H.

doi:10.1007/s40687-021-00310-2

Cited by 6 publications

(4 citation statements)

References 30 publications

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“…Then, using Theorem 3.7, we compute the ic-resurgence ρ ic (I) of I. For convenience, in this procedure we also include the function "rhoichypes" that was given in [20,Algorithm A.4…”

Section: Therefore It Suffices To Show That |Umentioning

confidence: 99%

“…The next result solves the problem of computing the ic-resurgence of I. An algorithm to compute ρ ic (I) has been implemented in Macaulay2 using its interface to Normaliz [8] (see [20,Procedure A.3,Algorithm A.4]). We use the next result to prove a duality formula for the ic-resurgence of I that implies the equality ρ ic (I) = ρ ic (I ∨ ).…”

Section: Introductionmentioning

confidence: 99%

“…Theorem 1.1. [20,Theorem 5.3] For each 1 ≤ j ≤ p, let ρ j be the optimal value of the following linear program with variables y 1 , . .…”

Section: Introductionmentioning

confidence: 99%

“…The first evidence that the equality ρ ic (I) = ρ ic (I ∨ ) could be true came from [13] and [20,25] where it is shown that for the edge ideal I(G) of a perfect graph G, one has…”

Section: Introductionmentioning

confidence: 99%

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A duality theorem for the ic-resurgence of edge ideals

Villarreal¹

2022

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The aim of this work is to use linear programming and polyhedral geometry to prove a duality formula for the ic-resurgence of edge ideals. We show that the ic-resurgence of the edge ideal I of a clutter C is equal to the ic-resurgence of the edge ideal I ∨ of the blocker C ∨ of C. We study the linear programs and the associated polyhedra that have been used to compute the ic-resurgence of squarefree monomial ideals. If C is a connected non-bipartite graph with a perfect matching or C is the clutter of bases of certain uniform matroids, we compute a formula for the ic-resurgence of I.

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“…Then, using Theorem 3.7, we compute the ic-resurgence ρ ic (I) of I. For convenience, in this procedure we also include the function "rhoichypes" that was given in [20,Algorithm A.4…”

Section: Therefore It Suffices To Show That |Umentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Theorem 1.1. [20,Theorem 5.3] For each 1 ≤ j ≤ p, let ρ j be the optimal value of the following linear program with variables y 1 , . .…”

Section: Introductionmentioning

confidence: 99%

“…The first evidence that the equality ρ ic (I) = ρ ic (I ∨ ) could be true came from [13] and [20,25] where it is shown that for the edge ideal I(G) of a perfect graph G, one has…”

Section: Introductionmentioning

confidence: 99%

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