Optimal transport for some symmetric, multidimensional integer partitions
Combinatorics
2023-10-17 v1 Number Theory
Optimization and Control
Abstract
A result of Hohloch links the theory of integer partitions with the Monge formulation of the optimal transport problem, giving the optimal transport map between (Young diagrams of) integer partitions and their corresponding symmetric partitions. Our aim is to extend Hohloch's result to the higher dimensional case. In doing so, we show the Kantorovich formulation of the optimal transport problem provides the tool to study the matching of higher dimensional partitions with their corresponding symmetric partitions.
Cite
@article{arxiv.2310.10474,
title = {Optimal transport for some symmetric, multidimensional integer partitions},
author = {Daniel Owusu Adu and Daniel Keliher},
journal= {arXiv preprint arXiv:2310.10474},
year = {2023}
}
Comments
10 pages, 4 figures, accepted for publication in Discrete Applied Mathematics