18 citations · 43 across the 34 of their papers we have counts for
5 papers · 1 filter
Some Wilf-equivalences for vincular patterns
Andrew M. Baxter, Mark Shattuck
We prove several Wilf-equivalences for vincular patterns of length 4, some of which generalize to infinite families of vincular patterns. We also present functional equations for t…
Congruence successions in compositions
Toufik Mansour, Mark Shattuck, Mark C. Wilson
A \emph{composition} is a sequence of positive integers, called \emph{parts}, having a fixed sum. By an \emph{-congruence succession}, we will mean a pair of adjacent parts …
Counting subwords in flattened permutations
Toufik Mansour, Mark Shattuck, David G. L. Wang
In this paper, we consider the number of occurrences of descents, ascents, 123-subwords, 321-subwords, peaks and valleys in flattened permutations, which were recently introduced b…
Recurrence relations for patterns of type in flattened permutations
Toufik Mansour, Mark Shattuck, David G. L. Wang
We consider the problem of counting the occurrences of patterns of the form within flattened permutations of a given length. Using symmetric functions, we find recurrence re…
On Multiple Pattern Avoiding Set Partitions
Vít Jelínek, Toufik Mansour, Mark Shattuck
We study classes of set partitions determined by the avoidance of multiple patterns, applying a natural notion of partition containment that has been introduced by Sagan. We say th…