English

Multiple Exchange Property for M$^\natural$-concave Functions and Valuated Matroids

Combinatorics 2017-04-12 v2

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.

Cite

@article{arxiv.1608.07021,
  title  = {Multiple Exchange Property for M$^\natural$-concave Functions and Valuated Matroids},
  author = {Kazuo Murota},
  journal= {arXiv preprint arXiv:1608.07021},
  year   = {2017}
}

Comments

10 pages

R2 v1 2026-06-22T15:30:08.266Z