4 citations · 7 across the 6 of their papers we have counts for
5 papers · 1 filter
Combinatorial Gray codes for classes of pattern avoiding permutations
W. M. B. Dukes, Mark F. Flanagan, Toufik Mansour +1
The past decade has seen a flurry of research into pattern avoiding permutations but little of it is concerned with their exhaustive generation. Many applications call for exhausti…
Wilf classification of three and four letter signed patterns
W. M. B. Dukes, T. Mansour, A. Reifegerste
We give some new Wilf equivalences for signed patterns which allow the complete classification of signed patterns of lengths three and four. The problem is considered for pattern a…
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…
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…
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…