INFINITE FAMILIES OF CONGRUENCES FOR OVERPARTITIONS WITH RESTRICTED ODD DIFFERENCES

摘要

Let (t) over bar (n) be the number of overpartitions in which (i) the di fference between successive parts may be odd only if the larger part is overlined and (ii) if the smallest part is odd then it is overlined. Ramanujan-type congruences for (t) over bar (n) modulo small powers of 2 and 3 have been established. We present two infinite families of congruences modulo 5 and 27 for (t) over bar (n), the first of which generalises a recent result of Chern and Hao ['Congruences for two restricted overpartitions', Proc. Math. Sci. 129 (2019), Article 31].