M. Shattuck

collaborators

6 papers

math.CO2025

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 $1$ in which each subsequent letter is at most one more than its predecessor. Let $C_{n}$ denote th…

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…

math.CO2025

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 $I ¨ = I ¨ _{1} \dots I ¨ _{n}$ such that $I ¨ _{i + r} - I ¨ _{i} \neq = s$ for all $1 \leq i \leq n - r$ , where $r$ and $s$ are fixed, was consider…

math.CO2025

Enumeration of consecutive patterns in flattened Catalan words

Mark Shattuck

A Catalan word $w$ is said to be flattened if the subsequence of $w$ obtained by taking the first letter of each weakly increasing run is nondecreasing. Let $F_{n}$ denote…

math.CO2025

Further Results for the Capacity Statistic Distribution on Compositions of 1's and 2's

Mark Shattuck

In this paper, we study additional aspects of the capacity distribution on the set $B_{n}$ of compositions of $n$ consisting of $1$ 's and $2$ 's. Among our results are furth…