For a permutation π = π1π2 · · · πn ∈ Sn and a positive integer i ≤ n, we can view π1π2 · · · πi as an element of Si by order-preserving relabeling. The j-set of ...
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...
W. M. B. Dukes, Toufik Mansour, Astrid Reifegerste
Let In() denote the number of involutions in the symmetric group Sn which avoid the permutation . We say that two permutations , Sj may be exchanged if for every n, k, and order...
We study the distribution of the statistics `number of fixed points' and `number of excedances' in permutations avoiding subsets of patterns of length 3. We solve all th...
Several authors have examined connections between restricted permutations and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for color...