Nayandeep Deka Baruah ; Hirakjyoti Das - Generating functions and congruences for 9-regular and 27-regular partitions in 3 colours

hrj:8927 - Hardy-Ramanujan Journal, January 9, 2022, Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021 - https://doi.org/10.46298/hrj.2022.8927
Generating functions and congruences for 9-regular and 27-regular partitions in 3 coloursArticle

Authors: Nayandeep Deka Baruah 1; Hirakjyoti Das ORCID1

Let b;3(n) denote the number of -regular partitions of n in 3 colours. In this paper, we find some general generating functions and new infinite families of congruences modulo arbitrary powers of 3 when {9,27}. For instance, for positive integers n and k, we haveb9;3(3kn+3k1)0 (mod 32k),b27;3(32k+3n+32k+4134)0 (mod 32k+5).


Volume: Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021
Published on: January 9, 2022
Accepted on: January 9, 2022
Submitted on: January 6, 2022
Keywords: l-regular partitions,Congruences,Generating functions,2010 Mathematics Subject Classification. 05A17; 11P83,[MATH]Mathematics [math]

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