Multiple Exchange Property for M$^\natural$-concave Functions and Valuated Matroids (1608.07021v2)

Published 25 Aug 2016 in math.CO

Abstract: The multiple exchange property for matroid bases is generalized for valuated matroids and M$^{\natural$-concave} set functions. The proof is based on the Fenchel-type duality theorem in discrete convex analysis. The present result has an implication in economics: The strong no complementarities (SNC) condition of Gul and Stacchetti is in fact equivalent to the gross substitutes (GS) condition of Kelso and Crawford.

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Authors (1)

Kazuo Murota

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