Displaying similar documents to “Congruences in ordered pairs of partitions.”

Self-conjugate vector partitions and the parity of the spt-function

George E. Andrews, Frank G. Garvan, Jie Liang (2013)

Acta Arithmetica

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Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first...

Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J

Chris Jennings-Shaffer (2016)

Acta Arithmetica

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We continue to investigate spt-type functions that arise from Bailey pairs. In this third paper on the subject, we proceed to introduce additional spt-type functions. We prove simple Ramanujan type congruences for these functions which can be explained by an spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting z = 1 in this definition. We find some of the spt-crank-type functions to have interesting representations...