Geodesic
Congruences modulo powers of 3 for generalized Frobenius partitions with six colors
Chao Gu1 ; Liuquan Wang2 ; Ernest X. W. Xia1
1 Department of Mathematics Jiangsu University Zhenjiang, Jiangsu 212013, P.R. China
2 Department of Mathematics National University of Singapore 10 Lower Kent Ridge Road Singapore, 119076, Singapore
Acta Arithmetica, Tome 175 (2016) no. 3, pp. 291-300.

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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 $c\phi _6(n)$.
DOI : 10.4064/aa8526-7-2016
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

Chao Gu 1 ; Liuquan Wang 2 ; Ernest X. W. Xia 1

1 Department of Mathematics Jiangsu University Zhenjiang, Jiangsu 212013, P.R. China
2 Department of Mathematics National University of Singapore 10 Lower Kent Ridge Road Singapore, 119076, Singapore 
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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. http://geodesic.mathdoc.fr/articles/10.4064/aa8526-7-2016/

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