On $(4, 5)$regular bipartitions with odd parts distinct
M. S. Mahadeva Naika, T. Harishkumar
In his work, K. Alladi considered the partition function $pod(n)$, the number of partitions of an integer $n$ with odd parts distinct (the even parts are unrestricted).
He obtained a series expansion for the product generating function of these partitions. Later Hirschhorn and Sellers obtained some internal congruences involving
the infinite families and Ramanujan's type congruences for $pod(n)$.
Let $B_{4, 5}(n)$ denote the number of $(4, 5)$regular bipartitions of a positive integer $n$ with odd parts distinct. In this paper, we establish many infinite families
of congruences modulo powers of $2$ for $B_{4, 5}(n)$.
Tbilisi Mathematical Journal, Vol. 12(3) (2019), pp. 191208
