On Simsun and Double Simsun Permutations Avoiding a Pattern of Length Three

Details On Simsun and Double Simsun Permutations Avoiding a Pattern of Length Three On Simsun and Double Simsun Permutations Avoiding a Pattern of Length Three

2010-04-22

arxiv.org/abs/1004.3964v1

Mathematics

Combinatorics

18 pages, 9 figures

Scientific paper

A permutation $\sigma\in\mathfrak{S}_n$ is simsun if for all $k$, the subword of $\sigma$ restricted to $\{1,...,k\}$ does not have three consecutive decreasing elements. The permutation $\sigma$ is double simsun if both $\sigma$ and $\sigma^{-1}$ are simsun. In this paper we present a new bijection between simsun permutations and increasing 1-2 trees, and show a number of interesting consequences of this bijection in the enumeration of pattern-avoiding simsun and double simsun permutations. We also enumerate the double simsun permutations that avoid each pattern of length three.

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