, Volume 30, Issue 3, pp 403-424

The crank of partitions mod 13

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Abstract

Let M(r,m,n) be the number of unrestricted partitions of n with crank congruent to r modulo m. Here the relations between the numbers M(r,13,13n+k) when 0≤r<13 are given. All of the results are proved by elementary methods.