Arithmetic properties of singular overpartition pairs without multiples of k

Purpose – In this paper, the author defines the function B¯i,jδ,k(n), the number of singular overpartition pairs of n without multiples of k in which no part is divisible by δ and only parts congruent to ± i, ± j modulo δ may be overlined. Design/methodology/approach – Andrews introduced to combinat...

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Bibliographic Details
Main Authors: S. Shivaprasada Nayaka, T.K. Sreelakshmi, Santosh Kumar
Format: Article
Language:English
Published: Emerald Publishing 2022-06-01
Series:Arab Journal of Mathematical Sciences
Subjects:
Online Access:https://www.emerald.com/insight/content/doi/10.1108/AJMS-01-2021-0013/full/pdf
Description
Summary:Purpose – In this paper, the author defines the function B¯i,jδ,k(n), the number of singular overpartition pairs of n without multiples of k in which no part is divisible by δ and only parts congruent to ± i, ± j modulo δ may be overlined. Design/methodology/approach – Andrews introduced to combinatorial objects, which he called singular overpartitions and proved that these singular overpartitions depend on two parameters δ and i can be enumerated by the function C¯δ,i(n), which gives the number of overpartitions of n in which no part divisible by δ and parts ≡ ± i(Mod δ) may be overlined. Findings – Using classical spirit of q-series techniques, the author obtains congruences modulo 4 for B¯2,48,3(n), B¯2,48,5 and B¯2,412,3. Originality/value – The results established in this work are extension to those proved in Andrews’ singular overpatition pairs of n.
ISSN:1319-5166
2588-9214