국가지식-학술정보
NEW CONGRUENCES FOR ℓ-REGULAR OVERPARTITIONS
- 대한수학회
- Journal of the Korean Mathematical Society
- Vol.59 No.5
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2022.01945 - 962 (18 pages)
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DOI : 10.4134/JKMS.j220011
- 0
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For a positive integer ℓ, <TEX>$ar{A}_{ell}(n)$</TEX> denotes the number of over-partitions of n into parts not divisible by ℓ. In this article, we find certain Ramanujan-type congruences for <TEX>$ar{A}_{r{ell}}(n)$</TEX>, when r ∈ {8, 9} and we deduce infinite families of congruences for them. Furthermore, we also obtain Ramanujan-type congruences for <TEX>$ar{A}_{13}(n)$</TEX> by using an algorithm developed by Radu and Sellers [15].
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