International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 759-768
-Color partitions with weighted differences equal to minus two
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 -color partitions of Agarwal and Andrews, 1987, in which
each pair of parts has weighted difference equal to 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 -color partitions. A combinatorial identity for self-conjugate -color
partitions is also obtained. We conclude by posing several open problems in the last section.