Note on the Polyhedral Description of the Minkowski Sum of Two L-convex Sets

Abstract

L-convex sets are one of the most fundamental concepts in discrete convex analysis. Furthermore, the Minkowski sum of two L-convex sets, called L 2 -convex sets, are the most intriguing objects that are closely related to polymatroid intersection. This paper reveals the polyhedral description of an L 2 -convex set, together with the observation that the convex hull of an L 2 -convex set is a box-TDI polyhedron. The proofs utilize Fourier-Motzkin elimination and the obtained results admit natural graph representations. Implications of the obtained results in discrete convex analysis are also discussed.