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Random partitions with non negative rth differences

Rod Canfield·Sylvie Corteel·Pawel Hitczenko
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Abstract

Let $P_r(n)$ be the set of partitions of n with non negative rth differences. Let $λ$ be a partition chosen uniformly at random among the set $P_r(n)$. Let $d(λ)$ be a positive rth difference chosen uniformly at random in $λ$. The aim of this work is to show that for every $m\ge 1$, the probability that $d(λ)\ge m$ approaches $m^{-1/r}$ as $n\to\infty$. To prove this result we use bijective, asymptotic/analytic, and probabilistic combinatorics.

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Rod Canfield, Sylvie Corteel, Pawel Hitczenko. 2001-10-17. Random partitions with non negative rth differences. https://arxiv.org/abs/math/0110188

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