A generalization of Franklin's partition identity and a Beck-type companion identity
Number Theory
2024-10-24 v1 Combinatorics
Abstract
Euler's classic partition identity states that the number of partitions of into odd parts equals the number of partitions of into distinct parts. We develop a new generalization of this identity, which yields a previous generalization of Franklin as a special case, and prove an accompanying Beck-type companion identity.
Keywords
Cite
@article{arxiv.2410.17378,
title = {A generalization of Franklin's partition identity and a Beck-type companion identity},
author = {Gabriel Gray and David Hovey and Brandt Kronholm and Emily Payne and Holly Swisher and Ren Watson},
journal= {arXiv preprint arXiv:2410.17378},
year = {2024}
}