no. 2
Ranks For Two Partition Quadruple Functions
Jennings-Shaffer, Chris1
1 Department of Mathematics Oregon State University Corvallis, Oregon 97331, USA
Journal de théorie des nombres de Bordeaux, Tome 29 (2017) no. 2, pp. 425-443.

L’auteur a récemment introduit deux fonctions de partitions entières qui satisfont des congruences du type Ramanujan modulo 3, 5, 7, et 13. On definit une statistique du type rang et obtient une amélioration de l’interprêtation combinatoire des congruences modulo 3, 5 et 7.

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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DOI : 10.5802/jtnb.986
Classification : 11P81, 11P83
Mots clés : Number theory, partitions, vector partitions, congruences, ranks, cranks
Jennings-Shaffer, Chris 1

1 Department of Mathematics Oregon State University Corvallis, Oregon 97331, USA 
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Jennings-Shaffer, Chris. Ranks For Two Partition Quadruple Functions. Journal de théorie des nombres de Bordeaux, Tome 29 (2017) no. 2, pp. 425-443. doi : 10.5802/jtnb.986. http://archive.numdam.org/articles/10.5802/jtnb.986/

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[2] Andrews, George E.; Berndt, Bruce C. Ramanujan’s lost notebook. Part III, Springer, 2012, xii+435 pages

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[8] Jennings-Shaffer, Chris Two partition functions with congruences modulo 3, 5, 7, and 13 (to appear in Ann. Comb.)

[9] Jennings-Shaffer, Chris Some Smallest Parts Functions from Variations of Bailey’s Lemma (2015) (https://arxiv.org/abs/1506.05344)

[10] Zwegers, Sander Mock theta functions, Utrecht University (2003) (Ph. D. Thesis https://dspace.library.uu.nl/handle/1874/878)

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