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...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
Emerald Publishing
2022-06-01
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Series: | Arab Journal of Mathematical Sciences |
Subjects: | |
Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-01-2021-0013/full/pdf |
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. |
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ISSN: | 1319-5166 2588-9214 |