Abstract
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.
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