Log-concavity of longest increasing subsequence
We prove a conjecture proposed by Chen that, for every fixed $n$, the sequence $(a_{n,k})_{k=1}^n$ is log-concave, where $a_{n,k}$ counts permutations of $[n]$ whose longest increasing subsequence has length $k$.
Authors
- Yupeng Li
Publication Details
- Journal
- arXiv (Cornell University)
- Published
- 2026-10-27
- DOI
- https://doi.org/10.48550/arxiv.2610.36483
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- preprint