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Published in last 50 years
We give a combinatorial proof of the first Rogers–Ramanujan identity by using two symmetries of a new generalization of Dyson's rank. These symmetries are established by direct bijections.
Generalizations of Dyson's rank and non-Rogers-Ramanujan partitions
Determinants [1] of 5th and 7th orders have already been discussed in connection with the Theorems 4 and 5 of Atkin and Swinnerton-Dyer [2]. The determinant under consideration occurs in the investigation of Dyson's rank function for q = 11 given by Atkin and Hussain [3]. As regards the notation it may be mentioned that the author has adopted the same as that of Atkin and Hussain [3].