Congruences modulo powers of 3 for generalized Frobenius partitions with six colors
Acta Arithmetica, Tome 175 (2016) no. 3, pp. 291-300
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
In his 1984 AMS Memoir, Andrews introduced the $k$-colored generalized Frobenius partition function. Let $c\phi _k(n)$ denote the number of generalized Frobenius partitions of $n$ with $k$ colors. Recently, congruences modulo 4, 9 and 27 for $c\phi _6(n)$ were proved by Baruah and Sarmah, Hirschhorn, and Xia. In this paper, we prove several congruences modulo powers of 3 for $c\phi _6(n)$ by using the generating function for $c\phi _6(3n+1)$ due to Hirschhorn. In particular, we confirm a conjecture on a congruence modulo 243 for $c\phi _6(n)$.
Keywords:
his ams memoir andrews introduced k colored generalized frobenius partition function phi denote number generalized frobenius partitions colors recently congruences modulo phi proved baruah sarmah hirschhorn xia paper prove several congruences modulo powers phi using generating function phi due hirschhorn particular confirm conjecture congruence modulo phi
Affiliations des auteurs :
Chao Gu 1 ; Liuquan Wang 2 ; Ernest X. W. Xia 1
@article{10_4064_aa8526_7_2016,
author = {Chao Gu and Liuquan Wang and Ernest X. W. Xia},
title = {Congruences modulo powers of 3 for generalized {Frobenius} partitions with six colors},
journal = {Acta Arithmetica},
pages = {291--300},
publisher = {mathdoc},
volume = {175},
number = {3},
year = {2016},
doi = {10.4064/aa8526-7-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8526-7-2016/}
}
TY - JOUR AU - Chao Gu AU - Liuquan Wang AU - Ernest X. W. Xia TI - Congruences modulo powers of 3 for generalized Frobenius partitions with six colors JO - Acta Arithmetica PY - 2016 SP - 291 EP - 300 VL - 175 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/aa8526-7-2016/ DO - 10.4064/aa8526-7-2016 LA - en ID - 10_4064_aa8526_7_2016 ER -
%0 Journal Article %A Chao Gu %A Liuquan Wang %A Ernest X. W. Xia %T Congruences modulo powers of 3 for generalized Frobenius partitions with six colors %J Acta Arithmetica %D 2016 %P 291-300 %V 175 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/aa8526-7-2016/ %R 10.4064/aa8526-7-2016 %G en %F 10_4064_aa8526_7_2016
Chao Gu; Liuquan Wang; Ernest X. W. Xia. Congruences modulo powers of 3 for generalized Frobenius partitions with six colors. Acta Arithmetica, Tome 175 (2016) no. 3, pp. 291-300. doi: 10.4064/aa8526-7-2016
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