Some properties of \(k\)-tuple \(t\)-core partitions (Q2240505)

Considering some properties of the Ramanujan's tau function and manipulations of \(q\)-series, the author proves several infinite families of congruences modulo powers of \(2\) and \(3\) for \(A_{3,9}(n)\), \(A_{9,3}(n)\), and \(A_{4,8}(n)\), where \(A_{t,k} (n)\) denote the number of \(k\)-tuple partitions of \(n\) where each partition is \(t\)-core.