Recently, Andrews considered the partitions with parts separated by parity, in which parts of a given parity are all smaller than those of the other parity. Inspired from the partitions with parts separated by parity, we investigate the overpartitions with separated overlined parts and non-overlined parts, in which the sizes of overlined parts (resp. non-overlined parts) are greater than or equal to those of non-overlined parts (resp. overlined parts).
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