PARTITION CONGRUENCES AND THE ANDREWS-GARVAN-DYSON CRANK

'''Partition Congruences and the Andrews-Garvan-Dyson Crank''' is a paper by Karl Mahlburg that was published in Proceedings of the National Academy of Sciences. It won the first PNAS Paper of the Year prize.
In 1944, Freeman Dyson conjectured the existence of a "crank" function
for partitions that would provide a combinatorial proof of Ramanujan's congruence
modulo 11. Forty years later, George Andrews and Garvan successfully found such a function
[3, 6], and proved the celebrated result that the crank simultaneously “explains” the
three Ramanujan congruences modulo 5, 7 and 11. This note announces the proof
[8] of a conjecture of Ono, which essentially asserts that the elusive crank satisfies
exactly the same types of general congruences as the partition function.
The full paper can be found at the links below.

Contents

External links

External links

★ Abstract

★ Partition Congruences and the Andrews-Garvan-Dyson Crank, Karl Mahlburg, , , Proceedings of the National Academy of Sciences, 2005