A Combinatorial Proof of an Identity for the Divisor Generating Function

[摘要] 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.

[学科分类] 离散数学和组合数学

[关键词] Uchimura's identity;Dilcher's identity;integer partition;arm length