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Some New Congruences for Andrews’ Singular Overpartition Pairs

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Abstract

In a recent work, Andrews defined the combinatorial objects called singular overpartitions denoted by \(\overline {C}_{k,i}(n)\), which count the number of overpartitions of n in which no part is divisible by k and only parts congruent to ± i modulo k may be overlined. Many authors have found congruences and infinite families of congruences modulo powers of 2 and 3. In this paper, we find some new infinite families of congruences for \(\overline {C}^{6}_{1,2}(n)\) modulo 27 and congruences modulo 4 for \(\overline {C}^{12}_{1,5}(n)\), \(\overline {C}^{9}_{3,3}(n)\) and \(\overline {C}^{15}_{5,5}(n)\).

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Acknowledgements

The authors would like to thank the anonymous referee for helpful comments and suggestions and the second author would like to thank UGC for providing National fellowship for higher education (NFHE), ref. no.F1-17.1/2015-16/NFST-2015-17-ST-KAR-1376.

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Authors and Affiliations

  1. Department of Mathematics, Bangalore University, Central College Campus, Bangalore, 560 001, Karnataka, India

    M. S. Mahadeva Naika & S. Shivaprasada Nayaka

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  1. M. S. Mahadeva Naika
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  2. S. Shivaprasada Nayaka
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Correspondence to M. S. Mahadeva Naika.

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Naika, M.S.M., Nayaka, S.S. Some New Congruences for Andrews’ Singular Overpartition Pairs. Vietnam J. Math. 46, 609–628 (2018). https://doi.org/10.1007/s10013-018-0271-5

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  • DOI: https://doi.org/10.1007/s10013-018-0271-5

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