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\(n\)-color partitions with weighted differences equal to minus two. (English) Zbl 0895.05005

Authors’ abstract: In this paper we study those \(n\)-color partitions of A. K. Agarwal and G. E. Andrews [J. Comb. Theory, Ser. A 45, 40-49 (1987; Zbl 0618.05003)], in which each pair of parts has weighted difference equal to –2. Results obtained in this paper for these partitions include several combinatorial identities, recurrence relations, generating functions, relationships with the divisor function and computer produced tables. By using these partitions an explicit expression for the sum of the divisors of odd integers is given. It is shown how these partitions arise in the study of conjugate and self-conjugate \(n\)-color partitions. A combinatorial identity for self-conjugate \(n\)-color partitions is also obtained. We conclude by posing several open problems in the last section.
Reviewer: J.Cigler (Wien)

MSC:

05A15 Exact enumeration problems, generating functions
05A17 Combinatorial aspects of partitions of integers
05A19 Combinatorial identities, bijective combinatorics
11B37 Recurrences
11P81 Elementary theory of partitions

Citations:

Zbl 0618.05003
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