A generalization of Franklin’s partition identity and a Beck-type companion identity

Authors

Gabriel Gray
David Hovey
Brandt Kronholm, The University of Texas Rio Grande Valley
Emily Payne, The University of Texas Rio Grande Valley
Holly Swisher
Ren Watson, University of Texas at Austin

Document Type

Article

Publication Date

7-16-2025

Abstract

Euler’s classic partition identity states that the number of partitions of n into odd parts equals the number of partitions of n 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.

Comments

Original published version available at https://doi.org/10.1007/s11139-025-01121-7

https://rdcu.be/eAK6g

Recommended Citation

Gray, Gabriel, David Hovey, Brandt Kronholm, Emily Payne, Holly Swisher, and Ren Watson. "A generalization of Franklin’s partition identity and a Beck-type companion identity: G. Gray et al." The Ramanujan Journal 67, no. 4 (2025): 100. https://doi.org/10.1007/s11139-025-01121-7

Publication Title

The Ramanujan Journal

DOI

10.1007/s11139-025-01121-7