Ranks For Two Partition Quadruple Functions
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 : https://doi.org/10.5802/jtnb.986
Classification : 11P81,  11P83
Mots clés : Number theory, partitions, vector partitions, congruences, ranks, cranks
@article{JTNB_2017__29_2_425_0,
     author = {Chris Jennings-Shaffer},
     title = {Ranks {For} {Two} {Partition} {Quadruple} {Functions}},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {425--443},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {29},
     number = {2},
     year = {2017},
     doi = {10.5802/jtnb.986},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.986/}
}
Chris Jennings-Shaffer. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.986/

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

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