On Brylawski's generalized duality
Combinatorics
2012-01-10 v1
Abstract
We introduce a notion of duality (due to Brylawski) that generalizes matroid duality to arbitrary rank functions. This generalized duality allows for generalized operations (deletion and contraction) and a generalized polynomial based on the matroid Tutte polynomial. This polynomial satisfies a deletion-contraction recursion. We explore this notion of duality for greedoids, antimatroids and demi-matroids, proving that matroids correspond precisely to objects that are simultaneously greedoids and "dual" greedoids.
Cite
@article{arxiv.1201.1831,
title = {On Brylawski's generalized duality},
author = {Gary Gordon},
journal= {arXiv preprint arXiv:1201.1831},
year = {2012}
}