Identities involving partitions with distinct odd parts and no parts congruent to 2 mod 4

2025/04/28 by Yi Shen, Shen, Yong-Chao
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2504.19727

openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, Pankaj Jyoti Mahanta and Manjil P. Saikika proved some identities relating certain restricted partitions into distinct odd parts with the partition whose odd parts are distinct combinatorially. They asked for the q-series proofs. In this paper, we give q-series proofs of these identities. Also, the number of partitions into distinct odd parts equals to the number of the partitions with no parts congruent to 2 mod 4, so we can get some identities. We also give combinatorial proofs of these identities.

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