Arithmetic of 2-regular partitions with distinct odd parts

2024/08/25 by Hemjyoti Nath, Nath, Hemjyoti
Mathematics · #05A17 #11F11 #11F20 #11P83 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Functional Equations Stability Results #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2408.13879

openalex publication_date 2024/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let pod₂(n) denote the number of 2-regular partitions of n with distinct odd parts (even parts are unrestricted). In this article, we obtain congruences for pod₂(n) mod 2 and mod 8 using some generating function manipulations and the theory of Hecke eigenform.

Related

• Identities involving partitions with distinct odd parts and no parts congruent to 2 mod 4
• New Congruences of Partitions With Odd Parts Distinct
• Congruences for Bipartitions with Odd Parts Distinct
• Generalizations of POD and PED partitions
• Congruences for the number of partitions and bipartitions with distinct even parts