Statistical structure of concave compositions
Combinatorics
2021-06-11 v3 Number Theory
Probability
Abstract
In this paper, we study concave compositions, an extension of partitions that were considered by Andrews, Rhoades, and Zwegers. They presented several open problems regarding the statistical structure of concave compositions including the distribution of the perimeter and tilt, the number of summands, and the shape of the graph of a typical concave composition. We present solutions to these problems by applying Fristedt's conditioning device on the uniform measure.
Cite
@article{arxiv.1605.00343,
title = {Statistical structure of concave compositions},
author = {Avinash J. Dalal and Amanda Lohss and Daniel Parry},
journal= {arXiv preprint arXiv:1605.00343},
year = {2021}
}
Comments
20 pages, 3 figures. Edited with helpful comments