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The spt-crank for overpartitions

Frank G. Garvan, Chris Jennings-Shaffer (2014)

Acta Arithmetica

Bringmann, Lovejoy, and Osburn (2009, 2010) showed that the generating functions of the spt-overpartition functions s p t ¯ ( n ) , s p t ¯ 1 ( n ) , s p t ¯ 2 ( n ) , and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and Liang (2012) defined an spt-crank in terms of weighted vector partitions which combinatorially explain simple congruences modulo 5 and 7 for spt(n). Chen, Ji, and Zang (2013) were able to define this spt-crank in terms of ordinary partitions. In this...

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