A tiling approach to eight identities of Rogers

Beginning in 1893, L.J. Rogers produced a collection of papers in which he considered series expansions of infinite products. Over the years, his identities have been given a variety of partition-theoretic interpretations and proofs. These existing combinatorial techniques, however, do not highlight the similarities and the subtle differences seen in so many of these remarkable identities. It is the goal of this paper to present a new combinatorial approach that unifies numerous q -series identities. The eight identities of Rogers that appear in G.E. Andrews’ 1986 CBMS monograph on q -series will serve as a basis for the collection of identities studied in this paper.