Abstract
Abstract
We obtain the asymptotic behaviour of the longest increasing/non-decreasing subsequences in a random uniform multiset permutation in which each element in
$\{1,\dots,n\}$
occurs k times, where k may depend on n. This generalises the famous Ulam–Hammersley problem of the case
$k=1$
. The proof relies on poissonisation and on a careful non-asymptotic analysis of variants of the Hammersley–Aldous–Diaconis particle system.
Publisher
Cambridge University Press (CUP)
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