Pattern Avoidance in Reserve Double Lists
In this paper, we consider pattern avoidance in a subset of words on t1, 1, 2, 2, . . . , n, nu 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 ¨ ¨ ¨ k-avoiders of maximum length for any positive integer k.
Anderson, Monica; Diepenbroek, Marika; Pudwell, Lara; and Stoll, Alex, "Pattern Avoidance in Reserve Double Lists" (2018). Mathematics and Statistics Faculty Publications. 60.