English

Maximum entropy and integer partitions

Combinatorics 2021-01-01 v1

Abstract

We derive asymptotic formulas for the number of integer partitions with given sums of jjth powers of the parts for jj belonging to a finite, non-empty set JNJ \subset \mathbb N. The method we use is based on the `principle of maximum entropy' of Jaynes. This principle leads to an intuitive variational formula for the asymptotics of the logarithm of the number of constrained partitions as the solution to a convex optimization problem over real-valued functions.

Keywords

Cite

@article{arxiv.2012.14498,
  title  = {Maximum entropy and integer partitions},
  author = {Gweneth McKinley and Marcus Michelen and Will Perkins},
  journal= {arXiv preprint arXiv:2012.14498},
  year   = {2021}
}