Generalisation of Keith's conjecture on \(9\)-regular partitions and \(3\)-cores

Authors

  • B. L. S. Lin Jimei University
  • A. Y. Z. Wang University of Electronic Science and Technology of China

Keywords:

regular partitions, congruences, 3-cores

Abstract

Recently, Keith used the theory of modular forms to study 9-regular partitions modulo 2 and 3. He obtained one infinite family of congruences modulo 3, and meanwhile proposed one analogous conjecture. In this note, we show that 9-regular partitions and 3-cores satisfy the same congruences modulo 3. Thus, we first derive several results on 3-cores, and then generalise Keith's conjecture and get a stronger result, which implies that all of Keith's results on congruences modulo 3 are consequences of our result. DOI: 10.1017/S0004972714000343

Published

2014-08-03

Issue

Vol. 90 No. 2 (2014)

Section

Articles
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