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Chris Jennings-Shaffer
Ranks For Two Partition Quadruple Functions
Journal de théorie des nombres de Bordeaux, 29 no. 2 (2017), p. 425-443, doi: 10.5802/jtnb.986
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Class. Math.: 11P81, 11P83
Keywords: Number theory, partitions, vector partitions, congruences, ranks, cranks

Résumé - Abstract

Recently the author introduced two new integer partition quadruple functions, which satisfy Ramanujan-type congruences modulo $3$, $5$, $7$, and $13$. Here we reprove the congruences modulo $3$, $5$, and $7$ by defining a rank-type statistic that gives a combinatorial refinement of the congruences.


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