Eric S. Egge ; Kailee Rubin - Snow Leopard Permutations and Their Even and Odd Threads

dmtcs:1279 - Discrete Mathematics & Theoretical Computer Science, June 1, 2016, Vol. 18 no. 2, Permutation Patterns 2015 -
Snow Leopard Permutations and Their Even and Odd ThreadsArticle

Authors: Eric S. Egge ; Kailee Rubin

    Caffrey, Egge, Michel, Rubin and Ver Steegh recently introduced snow leopard permutations, which are the anti-Baxter permutations that are compatible with the doubly alternating Baxter permutations. Among other things, they showed that these permutations preserve parity, and that the number of snow leopard permutations of length $2n-1$ is the Catalan number $C_n$. In this paper we investigate the permutations that the snow leopard permutations induce on their even and odd entries; we call these the even threads and the odd threads, respectively. We give recursive bijections between these permutations and certain families of Catalan paths. We characterize the odd (resp. even) threads which form the other half of a snow leopard permutation whose even (resp. odd) thread is layered in terms of pattern avoidance, and we give a constructive bijection between the set of permutations of length $n$ which are both even threads and odd threads and the set of peakless Motzkin paths of length $n+1$.

    Volume: Vol. 18 no. 2, Permutation Patterns 2015
    Section: Permutation Patterns
    Published on: June 1, 2016
    Submitted on: May 16, 2016
    Keywords: Mathematics - Combinatorics,05A05, 05A15

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