Congruences in ordered pairs of partitions

Hammond, Paul and Lewis, Richard (2004) Congruences in ordered pairs of partitions. International Journal of Mathematics and Mathematical Sciences, 2004 (47). pp. 2509-2512. ISSN 0161-1712

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Abstract

Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence p−1(n). The rank has been widely studied as have been other statistics, such as the crank. In this paper a “birank” is defined which relates to ordered pairs of partitions, and is used in an elementary proof of a congruence
in p−2(n)

Item Type: Article
Additional Information: The interested reader might also like to look at Frank Garvan's "Biranks for partitions into 2 colors" http://arxiv.org/pdf/0909.4892.pdf and http://www.math.ufl.edu/~fgarvan/papers/birank.pdf
Keywords: Partitions, rank, birank, Dyson, Ramanujan, congruence, combinatorial
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0101 Elementary mathematics. Arithmetic
Related URLs:
Depositing User: Paul Hammond
Date Deposited: 19 Nov 2012 06:42
Last Modified: 07 Mar 2017 05:53
URI: http://sro.sussex.ac.uk/id/eprint/42663

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