The free product of matroids

Authors:
Henry Crapo;William Schmitt
Affiliations:
-;-
Venue:
European Journal of Combinatorics
Year:
2005

Citing 0
Cited 6

A unique factorization theorem for matroids

Journal of Combinatorial Theory Series A
A matroid-friendly basis for the quasisymmetric functions

Journal of Combinatorial Theory Series A
Primitive elements in the matroid-minor Hopf algebra

Journal of Algebraic Combinatorics: An International Journal
Symmetric and quasi-symmetric functions associated to polymatroids

Journal of Algebraic Combinatorics: An International Journal
A quasisymmetric function for matroids

European Journal of Combinatorics
Splicing matroids

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

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.