Abstract:In 2017, Andrews, Dixit, Schultz and Yee introduced the function spt ω (n), which denotes the number of smallest parts in the overpartitions of n in which the smallest part is always overlined and all odd parts are less than twice the smallest part. Recently, Baruah and Begum established several internal congruences and congruences modulo small powers of 5 for spt ω (n). Moreover, they conjectured a family of internal congruences modulo any powers of 5 and two families of congruences modulo any even powers of … Show more
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