A Combinatorial Proof of an Identity for the Divisor Generating Function

Masanori Ando

Abstract


In this paper, we give combinatorial proofs and new generalizations of $q$-series identities of Dilcher and Uchimura related to divisor function. Some interesting combinatorial results related to partition and arm-length are also presented.


Keywords


Uchimura's identity; Dilcher's identity; integer partition; arm length

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