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ARITHMETIC PROPERTIES OF 3-REGULAR PARTITIONS IN THREE COLOURS

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  07 June 2021

ROBSON DA SILVA Open the ORCID record for ROBSON DA SILVA [Opens in a new window]  and
JAMES A. SELLERS
ROBSON DA SILVA*
Affiliation:
Departamento de Ciência e Tecnologia, Universidade Federal de São Paulo, Av. Cesare M. G. Lattes, 1201, São José dos Campos, SP, 12247-014, Brazil
JAMES A. SELLERS
Affiliation:
Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN 55812, USA e-mail: jsellers@d.umn.edu
*
e-mail: silva.robson@unifesp.br
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Abstract

Gireesh and Mahadeva Naika [‘On 3-regular partitions in 3-colors’, Indian J. Pure Appl. Math. 50 (2019), 137–148] proved an infinite family of congruences modulo powers of 3 for the function $p_{\{3,3\}}(n)$, the number of 3-regular partitions in three colours. In this paper, using elementary generating function manipulations and classical techniques, we significantly extend the list of proven arithmetic properties satisfied by $p_{\{3,3\}}(n).$

Keywords

partition3-regularthree colourscongruence

MSC classification

Primary: 11P83: Partitions; congruences and congruential restrictions
Secondary: 05A17: Partitions of integers

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 415 - 423
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

The first author was supported by the São Paulo Research Foundation (FAPESP) (grant no. 2019/14796-8).

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