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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| Format: | Article |
| Language: | English |
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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 |
| _version_ | 1797791669028913152 |
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| author | S. Shivaprasada Nayaka T.K. Sreelakshmi Santosh Kumar |
| author_facet | S. Shivaprasada Nayaka T.K. Sreelakshmi Santosh Kumar |
| author_sort | S. Shivaprasada Nayaka |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-13T02:22:09Z |
| format | Article |
| id | doaj.art-903b3644791d4e0a88eb82b49a6929e0 |
| institution | Directory Open Access Journal |
| issn | 1319-5166 2588-9214 |
| language | English |
| last_indexed | 2024-03-13T02:22:09Z |
| publishDate | 2022-06-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-903b3644791d4e0a88eb82b49a6929e02023-06-30T09:18:56ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142022-06-0128215216710.1108/AJMS-01-2021-0013Arithmetic properties of singular overpartition pairs without multiples of kS. Shivaprasada Nayaka0T.K. Sreelakshmi1Santosh Kumar2Department of Mathematics, BMS Institute of Technology and Management, Bengaluru, IndiaDepartment of Mathematics, BMS Institute of Technology and Management, Bengaluru, IndiaDepartment of Mathematics, BMS Institute of Technology and Management, Bengaluru, IndiaPurpose – 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.https://www.emerald.com/insight/content/doi/10.1108/AJMS-01-2021-0013/full/pdfCongruencesDissectionsSingular overpartition pairs without multiples of k |
| spellingShingle | S. Shivaprasada Nayaka T.K. Sreelakshmi Santosh Kumar Arithmetic properties of singular overpartition pairs without multiples of k Arab Journal of Mathematical Sciences Congruences Dissections Singular overpartition pairs without multiples of k |
| title | Arithmetic properties of singular overpartition pairs without multiples of k |
| title_full | Arithmetic properties of singular overpartition pairs without multiples of k |
| title_fullStr | Arithmetic properties of singular overpartition pairs without multiples of k |
| title_full_unstemmed | Arithmetic properties of singular overpartition pairs without multiples of k |
| title_short | Arithmetic properties of singular overpartition pairs without multiples of k |
| title_sort | arithmetic properties of singular overpartition pairs without multiples of k |
| topic | Congruences Dissections Singular overpartition pairs without multiples of k |
| url | https://www.emerald.com/insight/content/doi/10.1108/AJMS-01-2021-0013/full/pdf |
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