%0 Journal Article
%T On Simsun and Double Simsun Permutations Avoiding a Pattern of Length Three
%A Wan-Chen Chuang
%A Sen-Peng Eu
%A Tung-Shan Fu
%A Yeh-Jong Pan
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1004.3964v1