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Discrete Mathematics & Theoretical Computer Science |
Greta Panova - Bijective enumeration of permutations starting with a longest increasing subsequence
dmtcs:2829 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2829Bijective enumeration of permutations starting with a longest increasing subsequenceArticle
- 1 Harvard University [Cambridge]
- 2 Harvard University
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.
Source: HAL:hal-01186257v1
Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: permutations,longest increasing subsequence,q-analogue,major index,RSK,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
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