Schmidt-type theorems for partitions with uncounted parts

Abstract

Schmidt's theorem is significantly generalized, to partitions in which periodic but otherwise arbitrary subsets of parts are counted or uncounted. The identification of such sets of partitions with colored partitions satisfying certain specifications may be a generally useful tool for establishing sum-product $q$-series identities, examples of which are given.

21 pages; Thereom 3 generalized; recent citations added. Version to be submitted