AN INFINITE FAMILY OF CONGRUENCES FOR `-REGULAR OVERPARTITIONS

摘要

We consider new properties of the combinatorial objects known as overpartitions (which are natural generalizations of integer partitions). In particular, we establish an infinite set of Ramanujan-type congruences for the restricted overpartitions known as `-regular overpartitions. This significantly extends the recent work of Shen which focused solely on 3–regular overpartitions and 4–regular overpartitions.