eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2016-06-01
Vol. 18 no. 2, Permutation...
Permutation Patterns
10.46298/dmtcs.1279
1279
journal article
Snow Leopard Permutations and Their Even and Odd Threads
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 $n+1$.
https://dmtcs.episciences.org/1279/pdf
Mathematics - Combinatorics
05A05, 05A15