Name
Abstract | ||
|---|---|---|
For a subset $\cal{S}$ of positive integers let©(n,$\cal{S}$) be the set of partitions of ninto summands that are elements of $\cal{S}$. For every λε Ω(n,$\cal{S}$), letMn(λ) be the number of parts, withmultiplicity, that λ has. Put a uniform probabilitydistribution on Ω(n,$\cal{S}$), and regardMn as a random variable. In this paper thelimiting density of the (suitably normalized) random variableMn is determined for sets that aresufficiently regular. In particular, our results cover the case$\cal{S}$ = {;Q(k) : k ≥ 1}, whereQ(x) is a fixed polynomial of degree d ≥ 2.For specific choices of Q, the limiting density has appearedbefore in rather different contexts such as Kingman's coalescent,and processes associated with the maxima of Brownian bridge andBrownian meander processes. © 2007 Wiley Periodicals, Inc.Random Struct. Alg., 2008 |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1002/rsa.v32:4 | Random Struct. Algorithms |
Keywords | Field | DocType |
probability distribution,integer partition,limiting distribution,brownian bridge,random variable | Integer,Discrete mathematics,Combinatorics,Random variable,Brownian bridge,Polynomial,Uniform distribution (continuous),Multiplicity (mathematics),Partition (number theory),Maxima,Mathematics | Journal |
Volume | Issue | ISSN |
32 | 4 | 1042-9832 |
Citations | PageRank | References |
3 | 0.59 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| William M. Y. Goh | 1 | 37 | 9.89 |
| Pawel Hitczenko | 2 | 52 | 15.48 |