Bijective enumeration of permutations starting with a longest increasing subsequence

Greta Panova

Bijective enumeration of permutations starting with a longest increasing subsequence

Combinatorics 2010-06-17 v2

Authors: Greta Panova

Abstract

We prove a formula for the number of permutations in $S_n$ such that their first $n-k$ entries are increasing and their longest increasing subsequence has length $n-k$ . This formula first appeared as a consequence of character polynomial calculations in recent work of Adriano Garsia and Alain Goupil. We give two `elementary' bijective proofs of this result and of its $q$ -analogue, one proof using the RSK correspondence and one only permutations.

Keywords

permutations collatz conjecture integer sequences and recurrences

Cite

@article{arxiv.0905.2013,
  title  = {Bijective enumeration of permutations starting with a longest increasing subsequence},
  author = {Greta Panova},
  journal= {arXiv preprint arXiv:0905.2013},
  year   = {2010}
}

Comments

Revised version: added a bijection via permutations only, without RSK; incorporated referee's suggestions. To appear in DMTCS Proceedings

Bijective enumeration of permutations starting with a longest increasing subsequence

Abstract

Keywords

Cite

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