2016/07/31 by Xinhua Xiong, William J. Keith · 1 citation
Mathematics · #math.CO #msc:05A17 #msc:11P84
published as Ramanujan. J 2019 · 12 pages, revised version
arxiv created 2020/05/17 · arxiv updated 2020/05/19
In this paper, we give a conjecture, which generalises Euler's partition theorem involving odd parts and different parts for all moduli. We prove this conjecture for two family partitions. We give q-difference equations for the related generating function if the moduli is three. We provide new companions to Rogers-Ramanujan-Andrews-Gordon identities under this conjecture.