Freeman DysonAffiliation: Institute for Advanced Study Princeton Email: dyson@ias.edu Title Of Talk: Guesses and Proofs in the Theory of Partitions Abstract: Two disconnected remarks about partitions. First, a pedagogical remark connecting pure mathematics with statistical physics. The grand canonical ensemble of statistical mechanics is applied to the counting of partitions. This picture borrowed from physics gives a simple approximation to the exact calculation of the partition function by Hardy and Ramanujan. Second, some guesses are proposed for the spt-crank function defined in a recent paper by Andrews, Garvan and Liang. Here spt stands for smallest-part, and the spt-crank was designed to help us understand the beautiful new congruence properties of partition smallest-parts discovered by Andrews. The Andrews congruences are like the famous Ramanujan congruences of the partition function modulo 5, 7, and 11, except that Andrews has 13 mysteriously replacing 11.
Last update made Sun Oct 21 17:38:55 EDT 2012.
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