Geodesic
Pattern Avoidance in Reverse Double Lists
Discrete mathematics & theoretical computer science, Permutation Patterns 2016, Tome 19 (2017-2018) no. 2.

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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 $\rho$ of length 5 or more, we characterize when the number of $\rho$-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 $k$. 
@article{DMTCS_2018_19_2_a12,
     author = {Anderson, Monica and Diepenbroek, Marika and Pudwell, Lara and Stoll, Alex},
     title = {Pattern {Avoidance} in {Reverse} {Double} {Lists}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {19},
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     year = {2017-2018},
     doi = {10.23638/DMTCS-19-2-14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-14/}
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Anderson, Monica; Diepenbroek, Marika; Pudwell, Lara; Stoll, Alex. Pattern Avoidance in Reverse Double Lists. Discrete mathematics & theoretical computer science, Permutation Patterns 2016, Tome 19 (2017-2018) no. 2. doi : 10.23638/DMTCS-19-2-14. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-14/

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