International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 21, Pages 1097-1104
doi:10.1155/S0161171204206044
1974 conjecture of Andrews on partitions
Department of Studies in Mathematics, University of Mysore, Manasagangotri 570 006, Mysore, India
Received 13 June 2002
Copyright © 2004 Padmavathamma and M. R. Salestina. 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
The case k=a of the 1974 conjecture of Andrews on two
partition functions Aλ,k,a(n) and Bλ,k,a(n) was proved by the first author and Sudha (1993) and the
case k=a+1 was established by the authors (2000). In this
paper, we prove that the conjecture is false and give a revised
conjecture for a particular case when λ is even.