9 citations · 22 across the 9 of their papers we have counts for
9 papers
The area above the Dyck path of a permutation
Mark Dukes, Astrid Reifegerste
In this paper we study a mapping from permutations to Dyck paths. A Dyck path gives rise to a (Young) diagram and we give relationships between statistics on permutations and stati…
New equivalences for pattern avoiding involutions
Mark Dukes, Vit Jelínek, Toufik Mansour +1
We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove J…
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…
Permutation sign under the Robinson-Schensted-Knuth correspondence
Astrid Reifegerste
We show how the sign of a permutation can be deduced from the tableaux induced by the permutation under the Robinson-Schensted-Knuth correspondence. The result yields a simple proo…
Refined sign-balance on 321-avoiding permutations
Astrid Reifegerste
The number of even 321-avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the (n-1)/2th Catalan number otherwise. We present an in…
A generalization of the Simion-Schmidt bijection for restricted permutations
Astrid Reifegerste
We consider the two permutation statistics which count the distinct pairs obtained from the last two terms of occurrences of patterns t_1...t_{m-2}m(m-1) and t_1...t_{m-2}(m-1)m in…