Discrete Mathematics & Theoretical Computer Science |
In this paper, we consider pattern avoidance in a subset of words on {1,1,2,2,…,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⋯k-avoiders of maximum length for any positive integer k.