Characterizing the number of coloured m-ary partitions modulo m, with and without gaps

Abstract In a pair of recent papers, Andrews, Fraenkel and Sellers provide a complete characterization for the number of  m -ary partitions modulo  m , with and without gaps. In this paper we extend these results to the case of coloured  m -ary partitions, with and without gaps. Our method of proof is different, giving explicit expansions for the generating functions modulo  m .

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