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More cranks and t-cores

Published online by Cambridge University Press:  17 April 2009

F. G. Garvan
F. G. Garvan
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, United States of America, e-mail: frank@math.ufl.edu
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Abstract

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Dedicated to George Szekeres on the occasion of his 90th Birthday

In 1990, new statistics on partitions (called cransk) were found which combinatorially prove Ramanujan's congruences for the partition function modulo 5, 7, 11 and 25. The methods are extended to find cranks for Ramanujan's partition congruence modulo 49. A more explicit form of the crank is given for the modulo 25 congruence.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 379 - 391
Copyright
Copyright © Australian Mathematical Society 2001

References

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