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

2024/10/22 by G. B. Gray, Gray, Gabriel, David Hovey +9
Computer Science · Mathematics · #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Functional Equations Stability Results #Graph Labeling and Dimension Problems #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2410.17378

openalex publication_date 2024/10/22 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/28

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.

Related

• Refinements of Beck-type partition identities
• Beck-type companion identities for Franklin's identity
• On a Partition Identity of Lehmer
• A new generalization of the minimal excludant arising from an analogue of Franklin's identity
• Beck-type identities for Euler pairs of order r