MIT Combinatorics Seminar
The Andrews-Garvan-Dyson Crank and
Karl Mahlburg (MIT)
Wednesday, October 11, 2006 4:15 pm Room 2-136
In 1944 Freeman Dyson proposed the existence of a crank function that
combinatorially explain the Ramanujan congruences for the partition
call wasn't answered until 1987, when Garvan and Andrews devised a
interpretation of some interesting $q$-series in Ramanujan's "Lost
showed that this statistic decomposed the three congruences in a natural
However, in 2000 Ono revolutionized the
subject by proving the existence of infinite families of congruences,
question of finding combinatorial explanations for the new congruences.
work shows that the crank continues to act as a sort of "universal"
partition congruences, and satisfies exactly the same general congruence
the partition function.