ON COMBINATORIAL EXTENSIONS OF ROGERS-RAMANUJAN TYPE IDENTITIES

In the present paper we use anti-hook differences of Agarwal and Andrews as an elementary tool to provide new partition theoretic meanings to two generalized basic series in terms of ordinary partitions satisfying certain anti-hook difference conditions. Five particular cases are also discussed. These particular cases yield new partition theoretic versions of Gollnitz-Gordon identities and Gollnitz identity. Five q-identities of Rogers and three q-identities of Slater are further explored. These results extend the work of Goyal and Agarwal, Agarwal and Rana, and Sareen and Rana.