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

dmtcs:1489 - Discrete Mathematics & Theoretical Computer Science, June 1, 2016, Vol. 18 no. 2, Permutation Patterns 2015
Snow Leopard Permutations and Their Even and Odd Threads

Authors: Egge, Eric S. and Rubin, Kailee

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 $n+1$.


Source : oai:arXiv.org:1508.05310
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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