NEW CONGRUENCES FOR 3-REGULAR PARTITIONS WITH DESIGNATED SUMMANDS

摘要

In 2002, Andrews, Lewis and Lovejoy introduced and studied the partition function PD(n), the number of partitions of n with designated summands. Recently, congruences involving the number of `-regular partitions with designated summands, denoted by PD`(n), have been explored for ` = 2 and ` = 3. In this paper, we present new arithmetic properties of PD3(n), including a complete characterization of this function modulo 3.