n-Color partitions with weighted differences equal to minus two

• Main Authors: A. K. Agarwal, R. Balasubrananian
• Format: Article
• Language: English
• Published: Hindawi Limited 1997-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Subjects: partitions; combinatorial identities; recurrence relations; generating functions.
• Online Access: http://dx.doi.org/10.1155/S016117129700104X

In this paper we study those n-color partitions of Agarwal and Andrews, 1987, 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.