Combinatorial proofs of theorems of Merca on the sum of different parts congruent to r modulo m in all partitions of n

2023/03/12 by Cristina Ballantine, Ballantine, Cristina
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2303.06764

Abstract

We give combinatorial proofs of several recent results due to Merca on the sum of different parts congruent to r modulo m in all partitions of n. The proofs make use of some well known involutions from the literature and some new involutions introduced here.

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