# Journal of theKorean Mathematical SocietyJKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

## Article

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J. Korean Math. Soc. 2022; 59(4): 685-697

Published online July 1, 2022 https://doi.org/10.4134/JKMS.j210517

## On $3^k$-regular cubic partitions

Nayandeep Deka Baruah, Hirakjyoti Das

Tezpur University; Tezpur University

### Abstract

Recently, Gireesh, Shivashankar, and Naika \cite{GSN20} found some infinite classes of congruences for the 3- and the 9-regular cubic partitions modulo powers of 3. We extend their study to all the $3^k$-regular cubic partitions. We also find new families of congruences.

Keywords: Congruence, $m$-regular cubic partition

MSC numbers: Primary 05A17, 11P83

Supported by: The first author was partially supported by Grant no. MTR/2018/000157 of Science \& Engineering Research Board (SERB), DST, Government of India under the MATRICS scheme. The second author was partially supported by Council of Scientific \& Industrial Research (CSIR), Government of India under CSIR-JRF scheme.