International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 21-24, Pages 1097-1104
doi:10.1155/S0161171204206044

1974 conjecture of Andrews on partitions

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.