18 citations · 43 across the 34 of their papers we have counts for
40 papers
Distinct flattened partitions avoiding a pattern of length four
Toufik Mansour, Olivia Nabawanda, Mark Shattuck
Let denote the set of distinct permutations of length that arise from the flattening process applied to the partitions of . In this paper, w…
Distribution of the inversion statistic on run-sorted permutations
Toufik Mansour, Olivia Nabawanda, Mark Shattuck
Let be a permutation. We say that is - if and the entries immediately following the descent positions of form an increasing sequence.…
Combinatorial proofs of totals of some statistics on Catalan words
Mark Shattuck
A Catalan word is one on the alphabet of positive integers starting with in which each subsequent letter is at most one more than its predecessor. Let denote th…
On ascent sequences avoiding 021 and a pattern of length four
Toufik Mansour, Mark Shattuck
Ascent sequences of length avoiding the pattern are enumerated by the -th Catalan number . In this paper, we extend this result and enu…
Avoidance of vincular patterns by flattened derangements
Toufik Mansour, Mark Shattuck
In this paper, we consider the problem of avoiding a single vincular pattern of length three by derangements in the flattened sense and find explicit formulas for the generating fu…
Counting k-ary words by number of adjacency differences of a prescribed size
Sela Fried, Toufik Mansour, Mark Shattuck
Recently, the general problem of enumerating permutations such that for all , where and are fixed, was considered by…