On-Regular Bipartitions Modulo $m$

D D Somashekara (1) , K N Vidya

1 department of studies in mathematics, University of Mysore

Let $b_l (n)$ denote the number of $l$-regular partitions of $n$ and $B_l (n)$ denote the number of $l$-regular bipartitions of $n$. In this paper, we establish several infinite families of congruences satisfied by $B_l (n)$ for $l \in {2, 4, 7}$. We also establish a relation between $b_9 (2n)$ and $B_3 (n)$.

Mots clés: Congruence; partition; regular partition; regular bipartition; theta functions 2010 Mathematics Subject Classification 11P83; 05A17

Domaines: Mathématiques [math]; Théorie des nombres [math.NT]

D D Somashekara, K N Vidya. On-Regular Bipartitions Modulo $m$. Hardy-Ramanujan Journal, 2019, Atelier Digit_Hum, pp.50 - 57. ⟨10.46298/hrj.2019.5106⟩. ⟨hal-01986071⟩