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THE 7-REGULAR AND 13-REGULAR PARTITION FUNCTIONS MODULO 3

  • ERIC BOLL (a1) and DAVID PENNISTON (a2)
Abstract

Let $b_{\ell }(n)$ denote the number of $\ell$ -regular partitions of $n$ . In this paper we establish a formula for $b_{13}(3n+1)$ modulo $3$ and use this to find exact criteria for the $3$ -divisibility of $b_{13}(3n+1)$ and $b_{13}(3n)$ . We also give analogous criteria for $b_{7}(3n)$ and $b_{7}(3n+2)$ .

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eaboll@gmail.com
References
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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