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

  • Authors:

  • Wan-Chen Chuang;Sen-Peng Eu;Tung-Shan Fu;Yeh-Jong Pan

  • Affiliations:

  • (Correspd.) Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan, ROC, m0974103@mail.nuk.edu.tw/ speu@nuk.edu.tw;(Research partially supported by NSC grants 98-2115-M-390-002 (S.-P. Eu), 99-2115-M-251-001 (T.-S. Fu), and 99-2115-M-127-001 (Y.-J. Pan)) Department of Applied Mathematics, National University of ...;Mathematics Faculty, National Pingtung Institute of Commerce, Pingtung 900, Taiwan, ROC, tsfu@npic.edu.tw;Department of Computer Science and Information Engineering, Tajen University, Pingtung 907, Taiwan, ROC, yjpan@mail.tajen.edu.tw

  • Venue:
  • Fundamenta Informaticae - Lattice Path Combinatorics and Applications
  • Year:
  • 2012

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Abstract

A permutation σ ∈ $\frak{S}_n$ is simsun if for all k, the subword of σ restricted to {1, . . . , k} does not have three consecutive decreasing elements. The permutation σ is double simsun if both σ and σ−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.