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arXiv · 2201.08168

Pattern-avoidance and Fuss-Catalan numbers

Per Alexandersson·Samuel Asefa Fufa·Frether Getachew·Dun Qiu
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Abstract

We study a subset of permutations, where entries are restricted to having the same remainder as the index, modulo some integer $k \geq 2$. We show that when also imposing the classical 132- or 213-avoidance restriction on the permutations, we recover the Fuss--Catalan numbers and some special cases of the Raney numbers. Surprisingly, an analogous statement also holds when we impose the mod $k$ restriction on a Catalan family of subexcedant functions. Finally, we completely enumerate all combinations of mod-$k$-alternating permutations, avoiding two patterns of length 3. This is analogous to the systematic study by Simion and Schmidt, of permutations avoiding two patterns of length 3.

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Per Alexandersson, Samuel Asefa Fufa, Frether Getachew, Dun Qiu. 2022-01-20. Pattern-avoidance and Fuss-Catalan numbers. https://arxiv.org/abs/2201.08168

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