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- Henry Crapo
- J. Symb. Comput.
- 1991

- Henry Crapo, William Schmitt
- Eur. J. Comb.
- 2005

This paper is an initial inquiry into the structure of the Hopf algebra of matroids with restriction-contraction coproduct. Using a family of matroids introduced by Crapo in 1965, we show that the subalgebra generated by a single point and a single loop in the dual of this Hopf algebra is free.

- Henry Crapo, William Schmitt
- J. Comb. Theory, Ser. A
- 2005

- Henry Crapo, William Schmitt
- Eur. J. Comb.
- 2005

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)

- Alan Cheung, Henry Crapo
- J. Comb. Theory, Ser. B
- 1988

We introduce the matroid-minor coalgebra C, which has labeled matroids as distinguished basis, and coproduct given by splitting a matroid into a submatroid and complementary contraction all possible ways. We introduce two new bases for C; the first of these is is related to the distinguished basis by Möbius inversion over the rank-preserving weak order on… (More)

- Henry Crapo, William Schmitt
- J. Comb. Theory, Ser. A
- 2000

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)

- Henry Crapo
- 2003

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)

- Henry Crapo, Pierre Rosenstiehl
- Discrete Mathematics
- 2001

- Henry Crapo, Jean-Paul Laumond
- Geometry and Robotics
- 1988