  L-convex sets are one of the most fundamental concepts in discrete convex
analysis. Furthermore, the Minkowski sum of two L-convex sets, called L2-convex
sets, is an intriguing object that is closely related to polymatroid
intersection. This paper reveals the polyhedral description of an L2-convex
set, together with the observation that the convex hull of an L2-convex set is
a box-TDI polyhedron. Two different proofs are given for the polyhedral
description. The first is a structural short proof, relying on the conjugacy
theorem in discrete convex analysis, and the second is a direct algebraic
proof, based on Fourier-Motzkin elimination. The obtained results admit natural
graph representations. Implications of the obtained results in discrete convex
analysis are also discussed.
