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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(More)
The concept of matroid, with its companion concept of geometric lattice, was distilled by Hassler Whitney [19], Saunders Mac Lane [10] and Garrett Birkhoff [2] from the common properties of linear and algebraic dependence. The inverse problem, how to represent a given abstract matroid as the matroid of linear dependence of a specified set of vectors over(More)
This article summarizes the presently available general theory of rigidity of 3dimensional structures. We explain how a structure, for instance a bar and joint structure, can fail to be rigid for two quite different types of reasons. First, it may not have enough bars connecting certain sets of nodes. That is, it may faij for topologlcrl reasons. Secondly,.(More)