Rogers-Ramanujan Type Identities for Burge’s Restricted Partition Pairs Via Restricted Frobenius Partitions

We obtain generating functions for two sets of infinite families of restricted Frobenius partition functions by giving combinatorial arguments. We also establish a connection between three particular cases of these restricted Frobenius partition functions and Burge’s restricted partition pairs (J. Combin. Theory Ser. A, 63, 1993, 210–222). This connection and Burge’s Theorem 1 give us three new analytic identities. A comparison of these analytic identities with three known identities from Slater’s compendium (Proc. London Math. Soc. (2). 54, 1952, 147–167) leads us to Rogers-Ramanujan type identities for Burge’s restricted partition pairs.