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math.CO2021
Subregularity in infinitely labeled generating trees of restricted permutations
Toufik Mansour, Reza Rastegar, Mark Shattuck
In this paper, we revisit the application of generating trees to the pattern avoidance problem for permutations. In particular, we study this problem for certain general sets of pa…
math.CO2021
Pattern occurrences in -ary words revisited: a few new and old observations
Toufik Mansour, Reza Rastegar
In this paper, we study the pattern occurrence in -ary words. We prove an explicit upper bound on the number of -ary words avoiding any given pattern using a random walk argu…
math.CO2021
On column-convex and convex Carlitz polyominoes
Mansour Toufik, Reza Rastegar, Armend Shabani
In this paper, we introduce and study {\it Carlitz polyominoes}. In particular, we show that, as grows to infinity, asymptotically the number of \begin{enumerate} \item column-…