Department of Mathematics
University of Florida, Gainesville
Combinatorial interpretation of Ramanujan's partition congruences
Let p(n) denote the
number of unrestricted partitions of n. Ramanujan
discovered and later proved that p(5n+4) = 0 (mod 5), p(7n+5) = 0 (mod 7), p(11n+6) = 0 (mod 11). In my talk I describe various combinatorial interpretations of these congruences due to Dyson,
Andrews-Garvan and Garvan-Kim-Stanton. Finally, I discuss the Andrews-Stanley refinement of p(5n+4)
= 0 (mod 5) and briefly outline a new
combinatorial proof of this result. This
proof appears in my recent joint work with F. Garvan.