Robert OsburnAffiliation: University College Dublin Email: robert.osburn@ucd.ie Title Of Talk: $M_2$-rank differences for partitions without repeated odd parts Abstract: In 1944, Dyson initiated an important subject in the theory of partitions by discovering a simple statistic called the rank. He conjectured that the rank provided a combinatorial explanation for Ramanujan's congruences to the partition function modulo 5 and 7. In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures by establishing generating functions for rank differences in arithmetic progressions. In this talk, we combine the general idea of Atkin and Swinnerton-Dyer with some new q-series identities to prove analogous results for the M_2-rank of partitions without repeated odd parts. This is joint work with Jeremy Lovejoy.
Last update made Mon Mar 3 20:41:11 EST 2008.
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