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SOME INFINITE FAMILIES OF CONGRUENCES FOR OVERPARTITIONS WITH RESTRICTED ODD DIFFERENCES
Keywords:
Overpartitions, Congruences, Restricted odd differencesDOI:
https://doi.org/10.17654/0972555525027Abstract
Recently, Hanson and Smith [7] proved Ramanujan type congruences modulo 3 for $\bar{t}(n)$, where $\bar{t}(n)$ represents the number of overpartitions of $n$ with restricted odd differences. They also derived congruences modulo 5 for $\bar{t}(n)$. In this paper, we prove several infinite families of congruences modulo powers of 2 for $\bar{t}(n)$ by employing $q$-series identities and iterative computations.
Received: January 30, 2025
Revised: May 22, 2025
Accepted: July 14, 2025
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