Recurrences for permutations with long increasing subsequences

Manuel Kauers; Chen Wang

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arXiv · 2609.02220

Recurrences for permutations with long increasing subsequences

Manuel Kauers·Chen Wang

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Abstract

We prove two simple bivariate recurrences for the number of permutations with a long increasing subsequence. The two recurrences imply D-finiteness of the sequence in a certain range. As a consequence, we also obtain a proof of a conjecture posed by Kauers and Koutschan in 2023.

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BibTeX RIS

Manuel Kauers, Chen Wang. 2026-09-02. Recurrences for permutations with long increasing subsequences. https://arxiv.org/abs/2609.02220

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