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arXiv · 1704.08638

Pattern Avoidance in Reverse Double Lists

Monica Anderson·Marika Diepenbroek·Lara Pudwell·Alex Stoll
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Abstract

In this paper, we consider pattern avoidance in a subset of words on $\{1,1,2,2,\dots,n,n\}$ called reverse double lists. In particular a reverse double list is a word formed by concatenating a permutation with its reversal. We enumerate reverse double lists avoiding any permutation pattern of length at most 4 and completely determine the corresponding Wilf classes. For permutation patterns $ρ$ of length 5 or more, we characterize when the number of $ρ$-avoiding reverse double lists on $n$ letters has polynomial growth. We also determine the number of $1\cdots k$-avoiders of maximum length for any positive integer $k$.

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Monica Anderson, Marika Diepenbroek, Lara Pudwell, Alex Stoll. 2018-10-23. Pattern Avoidance in Reverse Double Lists. https://doi.org/10.23638/dmtcs-19-2-14

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