The Free product of Matroids
Combinatorics
2007-05-23 v1
Abstract
We introduce a noncommutative binary operation on matroids, called free product. We show that this operation respects matroid duality, and has the property that, given only the cardinalities, an ordered pair of matroids may be recovered, up to isomorphism, from its free product. We use these results to give a short proof of Welsh's 1969 conjecture, which provides a progressive lower bound for the number of isomorphism classes of matroids on an n-element set.
Keywords
Cite
@article{arxiv.math/0409080,
title = {The Free product of Matroids},
author = {Henry Crapo and William Schmitt},
journal= {arXiv preprint arXiv:math/0409080},
year = {2007}
}
Comments
5 pages, 1 figure. Accepted for publication in the European Journal of Combinatorics. See also arXiv:math.CO/0409028