On the number of simultaneous core partitions with $d$-distinct parts
Combinatorics
2019-08-19 v2
Abstract
We investigate the number of -core integer partitions with -distinct parts. Our first main result is a proof of a recurrence relation conjectured by Sahin in 2018. We also derive generating functions, asymptotics, and exact formulas for when is within of a multiple of . Finally, we exhibit a surprising connection to -restricted compositions.
Keywords
Cite
@article{arxiv.1807.08875,
title = {On the number of simultaneous core partitions with $d$-distinct parts},
author = {Noah Kravitz},
journal= {arXiv preprint arXiv:1807.08875},
year = {2019}
}