INFINITE FAMILIES OF CONGRUENCES MODULO 3 AND 9 FOR BIPARTITIONS WITH 3-CORES

Abstract

AbstractLet $A_{3}(n)$ denote the number of bipartitions of $n$ with 3-cores. Recently, Lin [‘Some results on bipartitions with 3-core’, J. Number Theory139 (2014), 44–52] established some congruences modulo 4, 5, 7 and 8 for $A_{3}(n)$. In this paper, we prove several infinite families of congruences modulo 3 and 9 for $A_{3}(n)$ by employing two identities due to Ramanujan.