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Acta Mathematica Sinica, English Series

, Volume 35, Issue 3, pp 355–368 | Cite as

On 3-Regular Tripartitions

  • Chandrashekar Adiga
  • Ranganatha DasappaEmail author
Article
  • 31 Downloads

Abstract

In this article, we investigate the arithmetic behavior of the function D3(n) which counts the number of 3-regular tripartitions of n. For example, we show that for α ≥ 1 and n ≥ 0,
$${D_3}\left( {{3^{2\alpha }}n + \frac{{11 \cdot {3^{2\alpha - 1}} - 1}}{4}} \right) \equiv 0\left( {\bmod {3^{2\alpha + 3}}} \right)$$
and
$${D_3}\left( {{3^{2\alpha }}n + \frac{{7 \cdot {3^{2\alpha - 1}} - 1}}{4}} \right) \equiv 0\left( {\bmod {3^{2\alpha + 2}}} \right)$$
.

Keywords

Regular partitions congruences theta functions 

MR(2010) Subject Classification

05A17 11P83 

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Notes

Acknowledgements

The authors thank the referee for his/her many valuable suggestions which enhanced the quality of presentation of this paper.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science (CAS), Chinese Mathematical Society (CAS) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Studies in MathematicsUniversity of MysoreManasagangotri, MysuruIndia
  2. 2.Department of Mathematics, School of Physical SciencesCentral University of KarnatakaKalaburagiIndia

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