Generalizations of Euler's Theorem to k-regular partitions

2025/11/18 by Lin, Hongshu, Zang, Wenston J. T. · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.14594

openalex publication_date 2025/11/18 · openalex created_date 2025/11/20 · openalex updated_date 2026/07/28

Abstract

Let A_k(n) denote the set of k-distinct partitions of n, and let B_k(n) be the set of k-regular partitions of n. Glaisher showed that # A_k(n) = # B_k(n). For k=2, this equality yields the celebrated Euler's partition theorem. In this paper, we present a new partition set E_k(n), which is equinumerous to B_k(n).

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• On Glaisher's Partition Theorem

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