Random partitions with non negative rth differences

Details Random partitions with non negative rth differences Random partitions with non negative rth differences

2001-10-17

arxiv.org/abs/math/0110188v1

Mathematics

Combinatorics

Scientific paper

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

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