English

A Stronger Multiple Exchange Property for M$^{\natural}$-concave Functions

Combinatorics 2017-06-29 v1

Abstract

The multiple exchange property for matroid bases has recently been generalized for valuated matroids and M^{\natural}-concave set functions. This paper establishes a stronger form of this multiple exchange property that imposes a cardinality condition on the exchangeable subset. The stronger form immediately implies the defining exchange property of M^{\natural}-concave set functions, which was not the case with the recently established multiple exchange property without the cardinality condition.

Cite

@article{arxiv.1706.09222,
  title  = {A Stronger Multiple Exchange Property for M$^{\natural}$-concave Functions},
  author = {Kazuo Murota},
  journal= {arXiv preprint arXiv:1706.09222},
  year   = {2017}
}
R2 v1 2026-06-22T20:32:04.047Z