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Higher Order SPT-Functions
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.Comment: 21 pages (previous version was 19 pages), added reference to Andrews
and Rose's recent paper, MacMahon's paper and OEIS, changed some wordin
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