[Abstract] F. G. Garvan; Biranks for Partitions into 2 Colors, Proceedings of Ramanujan Rediscovered 2009: A Conference in Memory of K. Venkatachaliengar on the Centenary of His Birth, Lecture Note Series of the Ramanujan Mathematical Society, to appear.

Dedicated to the memory of my friend Richard Lewis (1942 - 2007)


Abstract: In 2003, Hammond and Lewis defined a statistic on partitions into 2 colors which combinatorially explains certain well known partition congruences mod 5. We give two analogs of Hammond and Lewis's birank statistic. One analog is in terms of Dyson's rank and the second uses the 5-core crank due to Garvan, Kim and Stanton. We discuss Andrews's bicrank statistic and how it may be extended. We also generalize the Hammond-Lewis birank to a multirank for multipartitions and the Andrews bicrank to a multicrank for extended multipartitions. These both give combinatorial interpretations for multipartition congruences modulo all primes t>3.

The url of this page is http://www.math.ufl.edu/~frank/abstracts/birank.html.
Created by F.G. Garvan (fgarvan@ufl.edu) on Saturday, September 26, 2009.
Last update made Sat Sep 26 17:06:53 EDT 2009.

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