Abstract
Lovejoy introduced the partition function as the number of đ-regular overpartitions of đ. Andrews defined (đ, đ)-singular overpartitions counted by the partition function , and pointed out that . Meanwhile, Andrews derived an interesting divisibility property that (mod 3). Recently, we constructed the partition statistic đđ-crank of đ-regular overpartitions and give combinatorial interpretations for some congruences of as well as the congruences of Andrews. In this paper, we aim to prove some equalities for the đ3-crank of 3-regular overpartitions.
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