Recurrences for permutations with long increasing subsequences

2026-09-02

AI Summary

本文通过证明两个双变量递推关系解决了具有长递增子序列的排列计数问题，并在一定范围内证明了该序列的D-有限性，同时证实了一个相关猜想。

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.

Problem

• permutations
• increasing subsequences
• D-finiteness

Innovation

• bivariate recurrences
• long increasing subsequence
• D-finiteness