# Bijective enumeration of permutations starting with a longest increasing subsequence

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 :
Document type :
Conference papers
Domain :

Cited literature [2 references]

https://hal.inria.fr/hal-01186257
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Monday, August 24, 2015 - 3:45:32 PM
Last modification on : Tuesday, March 7, 2017 - 3:11:56 PM
Long-term archiving on: : Wednesday, November 25, 2015 - 7:53:59 PM

### File

dmAN0174.pdf
Publisher files allowed on an open archive

### Citation

Greta Panova. Bijective enumeration of permutations starting with a longest increasing subsequence. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.973-982, ⟨10.46298/dmtcs.2829⟩. ⟨hal-01186257⟩

Record views