Congruences modulo $4$ for the number of $3$-regular partitions
The last decade has seen an abundance of congruences for $b_\ell (n)$, the number of $\ell $-regular partitions of $n$. Notably absent are congruences modulo $4$ for $b_3(n)$. In this paper, we introduce Ramanujan type congruences modulo $4$ for $b_3(2n)$ involving some primes $p$ congruent to $ 11,...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.512/ |
| _version_ | 1797517885496623104 |
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| author | Ballantine, Cristina Merca, Mircea |
| author_facet | Ballantine, Cristina Merca, Mircea |
| author_sort | Ballantine, Cristina |
| collection | DOAJ |
| description | The last decade has seen an abundance of congruences for $b_\ell (n)$, the number of $\ell $-regular partitions of $n$. Notably absent are congruences modulo $4$ for $b_3(n)$. In this paper, we introduce Ramanujan type congruences modulo $4$ for $b_3(2n)$ involving some primes $p$ congruent to $ 11, 13, 17, 19, 23$ modulo $24$. |
| first_indexed | 2024-03-10T07:22:27Z |
| format | Article |
| id | doaj.art-afe215634f004e48888c3599e152f05e |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-10T07:22:27Z |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-afe215634f004e48888c3599e152f05e2023-11-22T14:31:30ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G91577158310.5802/crmath.51210.5802/crmath.512Congruences modulo $4$ for the number of $3$-regular partitionsBallantine, Cristina0Merca, Mircea1Department of Mathematics and Computer Science, College of The Holy Cross, Worcester, MA 01610, USAAcademy of Romanian Scientists, RO-050044, Bucharest, Romania; Department of Mathematical Methods and Models, Fundamental Sciences Applied in Engineering Research Center, University Politehnica of Bucharest, RO-060042 Bucharest, RomaniaThe last decade has seen an abundance of congruences for $b_\ell (n)$, the number of $\ell $-regular partitions of $n$. Notably absent are congruences modulo $4$ for $b_3(n)$. In this paper, we introduce Ramanujan type congruences modulo $4$ for $b_3(2n)$ involving some primes $p$ congruent to $ 11, 13, 17, 19, 23$ modulo $24$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.512/partitionsregular partitionscongruences |
| spellingShingle | Ballantine, Cristina Merca, Mircea Congruences modulo $4$ for the number of $3$-regular partitions Comptes Rendus. Mathématique partitions regular partitions congruences |
| title | Congruences modulo $4$ for the number of $3$-regular partitions |
| title_full | Congruences modulo $4$ for the number of $3$-regular partitions |
| title_fullStr | Congruences modulo $4$ for the number of $3$-regular partitions |
| title_full_unstemmed | Congruences modulo $4$ for the number of $3$-regular partitions |
| title_short | Congruences modulo $4$ for the number of $3$-regular partitions |
| title_sort | congruences modulo 4 for the number of 3 regular partitions |
| topic | partitions regular partitions congruences |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.512/ |
| work_keys_str_mv | AT ballantinecristina congruencesmodulo4forthenumberof3regularpartitions AT mercamircea congruencesmodulo4forthenumberof3regularpartitions |