Higher Order SPT-Functions

Details Higher Order SPT-Functions Higher Order SPT-Functions

2010-08-06

arxiv.org/abs/1008.1207v3

Mathematics

Number Theory

21 pages (previous version was 19 pages), added reference to Andrews and Rose's recent paper, MacMahon's paper and OEIS, chang

Scientific paper

Andrews' spt-function can be written as the difference between the second symmetrized crank and rank moment functions. Using the machinery of Bailey pairs a combinatorial interpretation is given for the difference between higher order symmetrized crank and rank moment functions. This implies an inequality between crank and rank moments that was only know previously for sufficiently large n and fixed order. This combinatorial interpretation is in terms of a weighted sum of partitions. A number of congruences for higher order spt-functions are derived.

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