4 citations · 7 across the 6 of their papers we have counts for
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math.CO2004★ 4 cited
The number of matroids on a finite set
W. M. B. Dukes
In this paper we highlight some enumerative results concerning matroids of low rank and prove the tail-ends of various sequences involving the number of matroids on a finite set to…
math.CO2004
Permutation statistics on involutions
W. M. B. Dukes
In this paper we look at polynomials arising from statistics on the classes of involutions, , and involutions with no fixed points, , in the symmetric group. Our results…
math.CO2004
Concerning the shape of a geometric lattice
W. M. B. Dukes
A well-known conjecture states that the Whitney numbers of the second kind of a geometric lattice (simple matroid) are logarithmically concave. We show this conjecture to be equiva…