Paper Info
Title
A Probabilistic Characterization of the Dominance Order on Partitions
Abstract
We present a probabilistic characterization of the dominance order on partitions. Let be a partition and its Ferrers diagram, i.e. a stack of rows of cells with row containing cells. Let the cells of be filled with independent and identically distributed draws from the random variable = (, ) with ≥ 1 and ∈ (0, 1). Given , ≥ 0, let (, , ) be the probability that the sum of all the entries in is while the sum of the entries in each row of is no more than . It is shown that if and are two partitions of , dominates if and only if (, , ) ≤ (, , ) for all , ≥ 0. It is shown that the same result holds if is any log-concave integer valued random variable with { : ( = ) > 0} = {0, 1,…,} for some ≥ 1.
Year
DOI
Venue
2018
https://doi.org/10.1007/s11083-017-9438-z
Order
Keywords
DocType
Volume
Dominance order,Majorization order,Riordan matrices,Total non-negativity,Pólya frequency sequences
Journal
35
Issue
Citations 
PageRank 
2
0
0.34
References 
Authors
1
1
Name
Order
Citations
PageRank
Clifford Smyth1246.91