Geodesic
Combinatoire, Théorie des nombres
Congruences modulo 4 for the number of 3-regular partitions
Ballantine, Cristina1  ; Merca, Mircea2, 3
1 Department of Mathematics and Computer Science, College of The Holy Cross, Worcester, MA 01610, USA
2 Department of Mathematical Methods and Models, Fundamental Sciences Applied in Engineering Research Center, University Politehnica of Bucharest, RO-060042 Bucharest, Romania
3 Academy of Romanian Scientists, RO-050044, Bucharest, Romania
Comptes Rendus. Mathématique, Tome 361 (2023) no. G9, pp. 1577-1583

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The last decade has seen an abundance of congruences for b ℓ (n), the number of ℓ-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.

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DOI : 10.5802/crmath.512
Classification : 11P83, 05A17, 11F33
Keywords: partitions, regular partitions, congruences

Ballantine, Cristina 1 ; Merca, Mircea 2, 3

1 Department of Mathematics and Computer Science, College of The Holy Cross, Worcester, MA 01610, USA
2 Department of Mathematical Methods and Models, Fundamental Sciences Applied in Engineering Research Center, University Politehnica of Bucharest, RO-060042 Bucharest, Romania
3 Academy of Romanian Scientists, RO-050044, Bucharest, Romania
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Ballantine, Cristina and Merca, Mircea},
     title = {Congruences modulo $4$ for the number of $3$-regular partitions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1577--1583},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     number = {G9},
     year = {2023},
     doi = {10.5802/crmath.512},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/crmath.512/}
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Ballantine, Cristina; Merca, Mircea. Congruences modulo $4$ for the number of $3$-regular partitions. Comptes Rendus. Mathématique, Tome 361 (2023) no. G9, pp. 1577-1583. doi: 10.5802/crmath.512

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