Conference proceeding
Random partitions with parts in the range of a polynomial
Society for Industrial and Applied Mathematics. Proceedings of the Workshop on Analytic Algorithmics and Combinatorics (ANALCO), Vol.273
01 Jan 2006
Abstract
Let Ω(n,Q) be the set of partitions of n into summands that are elements of the set A = {Q(k) : k ∈ Z^sup +^}. Here Q ∈ Z[x] is a fixed polynomial of degree d > 1 which is increasing on R^sup +^, and such that Q(m) is a non-negative integer for every integer m ≥ 0. For every λ ∈ Ω(n,Q), let M^sub n^(λ) be the number of parts, with multiplicity, that λ has. Put a uniform probability distribution on Ω(n,Q), and regard M^sub n^ as a random variable. The limiting density of the random variable M^sub n^ (suitably normalized) is determined explicitly. For specific choices of Q, the limiting density has appeared before in rather different contexts such as Kingman's coalescent, and processes associated with the maxima of Brownian bridge and Brownian meander processes. [PUBLICATION ABSTRACT]
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Details
- Title
- Random partitions with parts in the range of a polynomial
- Creators
- William GohPawel Hitczenko
- Publication Details
- Society for Industrial and Applied Mathematics. Proceedings of the Workshop on Analytic Algorithmics and Combinatorics (ANALCO), Vol.273
- Conference
- Society for Industrial and Applied Mathematics. Workshop on Analytic Algorithmics and Combinatorics (ANALCO)
- Publisher
- Society for Industrial and Applied Mathematics
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- [Retired Faculty]; Mathematics
- Identifiers
- 991019170567604721