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-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-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}
}