International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 759-768

n-Color partitions with weighted differences equal to minus two

A. K. Agarwal1 and R. Balasubrananian2

1Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Jawahar Nagar, Khanapara, Guwahati 781022, India
2The Institute of Mathematical Sciences, C I T. Campus, Madras 600 113, India

Received 6 November 1995

Copyright © 1997 A. K. Agarwal and R. Balasubrananian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.