Work of Professor Qing Ji
The Göllnitz-Gordon identity is one of the famous combinatorial identities in the theory of partitions. In 1967, Andrews proved a generalization of this theorem, known as the Andrews-Göllnitz-Gordon identity. The analytical counterpart of the generalized result was proved by Bressoud in 1980. In recent years, many overpartition analogues of classical partition theorems have been proved. Lovejoy obtained an overpartition analogue of the Andrews-Göllnitz-Gordon theorem for i=k.
In this paper, we give an overpartition analogue of the Andrews-Göllnitz-Gordon theorem for k≥i≥1 and its analytical counterpart. In doing so, we introduced a new concept, Göllnitz-Gordon marking, and then established two combinatorial identities based on the definition of Göllnitz-Gordon marking. The analytical identity is obtained by using Bailey pairs.
Main References:
[1] G.E. Andrews, A generalization of the Göllnitz-Gordon partition theorem, Proc.
Amer. Math. Soc. 18 (1967) 945-952.
[2] J. Lovejoy, Overpartition theorems of the Rogers-Ramanujan type, J. Lond. Math. Soc. 69 (2004) 562–574.
J COMB THEORY A
https://doi.org/10.1016/j.jcta.2019.02.021
