Infinite families of infinite families of congruences for k-regular partitions

Abstract

Let k∈{10,15,20}, and let b k (n) denote the number k-regular partitions of n. We prove for half of all primes p and any t≥1 that there exist p−1 arithmetic progressions modulo p 2t such that b k (n) is a multiple of 5 for each n in one of these progressions.

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Acknowledgements

The first author thanks the Wake Forest Undergraduate Research Fellowship Program for funding. The authors also thank Jeremy Rouse for his helpful comments during the development of this paper.

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Correspondence to John J. Webb.

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Carlson, R., Webb, J.J. Infinite families of infinite families of congruences for k-regular partitions. Ramanujan J 33, 329–337 (2014). https://doi.org/10.1007/s11139-013-9523-x

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Keywords

  • Partitions
  • Modular forms
  • Congruences for modular forms

Mathematics Subject Classification (2010)

  • 11F11
  • 11P83