5 citations · 7 across the 4 of their papers we have counts for
7 papers · 1 filter
Periodic de Bruijn triangles: exact and asymptotic results
B. Shapiro, M. Shapiro, A. Vainshtein
We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic for…
Counting occurences of 132 in a permutation
Toufik Mansour, Alek Vainshtein
We study the generating function for the number of permutations on n letters containing exactly $r\gs0$ occurences of 132. It is shown that finding this function for a given r amou…
Restricted 132-avoiding permutations
T. Mansour, A. Vainshtein
We study generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation on k letters, or containing exactly once. In several int…
Restricted permutations and Chebyshev polynomials
T. Mansour, A. Vainshtein
We study generating functions for the number of permutations in $\SS_n$ subject to two restrictions. One of the restrictions belongs to $\SS_3$, while the other to $\SS_k$. It turn…
Layered restrictions and Chebyshev polynomials
T. Mansour, A. Vainshtein
A permutation is called layered if it consists of the disjoint union of substrings (layers) so that the entries decrease within each layer, and increase between the layers. We find…
Avoiding maximal parabolic subgroups of S_k
Toufik Mansour, Alek Vainshtein
We find an explicit expression for the generating function of the number of permutations in S_n avoiding a subgroup of S_k generated by all but one simple transpositions. The gener…