Dyson's crank and unimodal compositions
Combinatorics
2022-03-07 v1 Number Theory
Abstract
The crank is a partition statistic requested by Dyson in 1944 in order to combinatorially prove a Ramanujan congruence of Euler's partition function . In this paper, we provide connections between Dyson's crank and unimodal compositions. Somewhat unrelated, we give a combinatorial proof of a new truncated Euler pentagonal number theorem due to Xia and Zhao.
Cite
@article{arxiv.2203.02061,
title = {Dyson's crank and unimodal compositions},
author = {Cristina Ballantine and Mircea Merca},
journal= {arXiv preprint arXiv:2203.02061},
year = {2022}
}
Comments
14 pages