Abstract
Let \(A_{t,k}(n)\) denote the number of partition k-tuples of n where each partition is t-core. In this paper, we prove some Ramanujan-type congruences for the partition function \(A_{t,k}(n)\) when \((t,k)=(3,4)\), (3,9), (4,8), (5, 6), (8, 4), (9, 3) and (9, 6) by employing q-series identities.
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The authors are extremely grateful to the anonymous referee for his/her valuable suggestions and comments.
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The corresponding author (N. Saikia) thanks Council of Scientific and Industrial Research of India for partially supporting the research work under the Research Scheme No. 25(0241)/15/EMR-II (F. No. 25(5498)/15).
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Saikia, N., Boruah, C. New congruences for k-tuples t-core partitions. J Anal 26, 27–37 (2018). https://doi.org/10.1007/s41478-017-0065-2
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DOI: https://doi.org/10.1007/s41478-017-0065-2