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arXiv · 0905.2013

Bijective enumeration of permutations starting with a longest increasing subsequence

Greta Panova
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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.

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Greta Panova. 2010-06-16. Bijective enumeration of permutations starting with a longest increasing subsequence. https://arxiv.org/abs/0905.2013

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