Frank Garvan

Affiliation: University of Florida

Email: frank@math.ufl.edu

Title Of Talk: The Rank and Crank of Partitions - In Memory of Richard P. Lewis

URL: http://qseries.org/fgarvan/rankcrank.html

Abstract: In this talk we examine the problem of exact linear relations for the rank and the crank of partitions as well as the problem of congruence relations. This talk is in memory of Richard Lewis and highlights some of his work. The first linear relations were found for the rank mod 5 and 7 by Dyson (1944) although the mod 5 results are encoded in an identity in Ramanujan's Lost Notebook. The first congruence relations for the rank were found by Atkin and Hussain (1958). We also give three ranks for 2-colored partitions which were inspired by a paper of Lewis and Hammond (2004).

Last update made Wed Mar 5 20:21:12 EST 2008.
Please report problems to: frank@math.ufl.edu