Extensions and variations of Andrews-Merca identities

2022/05/07 by Darlison Nyirenda, Nyirenda, Darlison, Beaullah Mugwangwavari +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2205.03697

openalex publication_date 2022/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, Andrews and Merca have given a new combinatorial interpretation of the total number of even parts in all partitions of n into distinct parts. We generalise this result and consider many more variations of their work. We also highlight some connections with the work of Fu and Tang.

Related

• Combinatorial proofs of several partition identities of Andrews and Merca
• Combinatorial meaning of the number of the even parts in a partition of n into distinct parts
• A bijection proof of Andrews-Merca integer partition theorem
• Combinatorial proof of identities involving partitions with distinct even parts and 4-regular partitions
• Combinatorial proofs of two Euler type identities due to Andrews