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Congruences for 9-regular partitions modulo 3

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Abstract

It is proved that the number of 9-regular partitions of n is divisible by 3 when n is congruent to 3 mod 4, and by 6 when n is congruent to 13 mod 16. An infinite family of congruences mod 3 holds in other progressions modulo powers of 4 and 5. A collection of conjectures includes two congruences modulo higher powers of 2 and a large family of “congruences with exceptions” for these and other regular partitions mod 3.

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  1. Fisher Hall 316, 1400 Townsend Drive, Houghton, MI, 49931, USA

    William J. Keith

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  1. William J. Keith
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Keith, W.J. Congruences for 9-regular partitions modulo 3. Ramanujan J 35, 157–164 (2014). https://doi.org/10.1007/s11139-013-9522-y

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