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REFINEMENTS OF THE FIRST AND SECOND POSITIVE CRANK MOMENTS
Published online by Cambridge University Press: 17 February 2016
Abstract
We revisit Berkovich and Garvan’s two bijections: the first gives symmetry of cranks and the second relates partitions with crank $\leq k$ to those with $k$ in the rank-set of partitions. Using these, we give a combinatorial proof for the relationship between the first positive crank moment and the sum of sizes of Durfee squares. We also study refinements of the first and second positive crank moments.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 94 , Issue 2 , October 2016 , pp. 236 - 244
- Copyright
- © 2016 Australian Mathematical Publishing Association Inc.