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



Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Jawahar Nagar, Khanapara, Guwahati 781022, India

The Institute of Mathematical Sciences, C I T. Campus, Madras 600 113, India

Received 6 November 1995

Copyright © 1997 Hindawi Publishing Corporation. 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.

Abstract

In this paper we study those n-color partitions of Agarwal and Andrews, 1987, in whicheach pair of parts has weighted difference equal to −2 Results obtained in this paper for thesepartitions include several combinatorial identities, recurrence relations, generating functions, relationshipswith the divisor function and computer produced tables. By using these partitions an explicit expressionfor the sum of the divisors of odd integers is given. It is shown how these partitions arise in the study ofconjugate and self-conjugate n-color partitions. A combinatorial identity for self-conjugate n-colorpartitions is also obtained. We conclude by posing several open problems in the last section.





Autor: A. K. Agarwal and R. Balasubrananian

Fuente: https://www.hindawi.com/



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