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Congruences for (3,11)-regular bipartitions modulo 11

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Abstract

In this note we investigate the function \(B_{k,\ell }(n)\), which counts the number of \((k,\ell )\)-regular bipartitions of n. We shall prove an infinite family of congruences modulo 11: for \(\alpha \ge 2\) and \(n\ge 0\),

$$\begin{aligned} B_{3,11}\left( 3^{\alpha }n+\frac{5\cdot 3^{\alpha -1}-1}{2}\right) \equiv 0\ (\mathrm{mod\ }11). \end{aligned}$$

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Acknowledgments

The author would like to thank the referee for helpful comments and valuable suggestions.

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Authors and Affiliations

  1. School of Mathematics, Jilin University, Changchun, 130012, Jilin, People’s Republic of China

    Donna Q. J. Dou

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  1. Donna Q. J. Dou
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Correspondence to Donna Q. J. Dou.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11201176).

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Dou, D.Q.J. Congruences for (3,11)-regular bipartitions modulo 11. Ramanujan J 40, 535–540 (2016). https://doi.org/10.1007/s11139-015-9732-6

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