The Ulam-Hammersley problem for multiset permutations
Combinatorics
2025-04-08 v4 Probability
Abstract
We obtain the asymptotic behaviour of the longest increasing/non-decreasing subsequences in a random uniform multiset permutation in which each element in {1,...,n} occurs k times, where k may depend on n. This generalizes the famous Ulam-Hammersley problem of the case k=1. The proof relies on poissonization and a connection with variants of the Hammersley-Aldous-Diaconis particle system.
Cite
@article{arxiv.2301.02557,
title = {The Ulam-Hammersley problem for multiset permutations},
author = {Lucas Gerin},
journal= {arXiv preprint arXiv:2301.02557},
year = {2025}
}