Abstract
Let \(\text {pod}_{9}(n)\), \(\text {ped}_{9}(n)\), and \(\overline {A}_{9}(n)\) denote the number of 9-regular partitions of n wherein odd parts are distinct, even parts are distinct, and the number of 9-regular overpartitions of n, respectively. By considering \(\text {pod}_{9}(n)\) from an arithmetic point of view, we establish a number of infinite families of congruences modulo 16 and 32, and some internal congruences modulo small powers of 3. A relation connecting above partition functions in arithmetic progressions is obtained as follows. For any \(n\geq 0\),
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Acknowledgements
The authors would like to thank anonymous referee for his/her valuable comments.
Funding
The second author was supported by the Council of Scientific and Industrial Research, India through SRF (No. 09/039(0111)/2014-EMR-I).
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Hemanthkumar, B., Bharadwaj, H.S.S. & Naika, M.S.M. Arithmetic Properties of 9-Regular Partitions with Distinct Odd Parts. Acta Math Vietnam 44, 797–811 (2019). https://doi.org/10.1007/s40306-018-0274-z
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DOI: https://doi.org/10.1007/s40306-018-0274-z