A duality theorem for the ic-resurgence of edge ideals. (March 2023)

• Record Type: Journal Article
• Authors: Villarreal, Rafael H.
• Is Part Of: European journal of combinatorics. Volume 109(2023)
• Publication Date: 2023-03
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2022.103656
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: 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 and the ic-resurgence of the edge ideal I ∨ of the blocker C ∨ of C coincide. If C is the clutter of bases of certain uniform matroids, we recover a formula for the resurgence of I, and if C is a connected non-bipartite graph with a perfect matching, we show a formula for the Waldschmidt constant of I ∨ .