Toufik Mansour

collaborators

4 papers

math.CO2026

Distinct flattened partitions avoiding a pattern of length four

Toufik Mansour, Olivia Nabawanda, Mark Shattuck

Let $P_{n}$ denote the set of distinct permutations of length $n$ that arise from the flattening process applied to the partitions of $[n] = {1, \dots, n}$ . In this paper, w…

math.CO2026

Distribution of the inversion statistic on run-sorted permutations

Toufik Mansour, Olivia Nabawanda, Mark Shattuck

Let $π = π_{1} \dots π_{n}$ be a permutation. We say that $π$ is $r u n$ - $sor t e d$ if $π_{1} = 1$ and the entries immediately following the descent positions of $π$ form an increasing sequence.…

math.CO2025

On ascent sequences avoiding 021 and a pattern of length four

Toufik Mansour, Mark Shattuck

Ascent sequences of length $n$ avoiding the pattern $021$ are enumerated by the $n$ -th Catalan number $C_{n} = \frac{1}{n + 1} (n 2 n)$ . In this paper, we extend this result and enu…

math.CO2025

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…