Congruences modulo $4$ for the number of $3$-regular partitions

Cristina Ballantine; Mircea Merca

doi:10.5802/crmath.512

Combinatoire, Théorie des nombres

Congruences modulo

4

for the number of

3

-regular partitions

Cristina Ballantine ¹ ; Mircea Merca ^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

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1577-1583.

Résumé

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 $b_{3} (2 n)$ involving some primes $p$ congruent to $11, 13, 17, 19, 23$ modulo $24$ .

Reçu le : 2023-03-14
Révisé le : 2023-04-19
Accepté le : 2023-05-06
Publié le : 2023-11-10

DOI : 10.5802/crmath.512

Classification : 11P83, 05A17, 11F33
Mots clés : partitions, regular partitions, congruences

Affiliations des auteurs :

Cristina Ballantine ¹ ; Mircea Merca ^{2, 3}

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Cristina Ballantine and Mircea Merca},
     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},
     year = {2023},
     doi = {10.5802/crmath.512},
     language = {en},
}

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Cristina Ballantine; Mircea Merca. Congruences modulo $4$ for the number of $3$-regular partitions. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1577-1583. doi : 10.5802/crmath.512. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.512/

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