INFINITE FAMILIES OF CONGRUENCES FOR OVERPARTITIONS WITH RESTRICTED ODD DIFFERENCES

Let $\overline{t}(n)$ be the number of overpartitions in which (i) the difference 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 $\overline{t}(n)$ modulo small powers of $2$ and $3$ ha...

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2020-08, Vol.102 (1), p.59-66
Hauptverfasser: LIN, BERNARD L. S., LIU, JIAN, WANG, ANDREW Y. Z., XIAO, JIEJUAN
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Sprache:eng
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Zusammenfassung:Let $\overline{t}(n)$ be the number of overpartitions in which (i) the difference 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 $\overline{t}(n)$ modulo small powers of $2$ and $3$ have been established. We present two infinite families of congruences modulo $5$ and $27$ for $\overline{t}(n)$, the first of which generalises a recent result of Chern and Hao [‘Congruences for two restricted overpartitions’, Proc. Math. Sci. 129 (2019), Article 31].
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972719001254