Euler's partition theorem for all moduli and new companions to   Rogers-Ramanujan-Andrews-Gordon identities
  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. 
Xinhua Xiong and William J. Keith
math.CO