Kathiravan T.

Institute of Mathematical Sciences · Department of Mathematics

Let $b_{\ell, k}(n), b_{\ell, k, r}(n)$ count the number of $(\ell, k)$, $(\ell, k, r)$-regular partitions respectively. In this paper we shall derive infinite families of congruences for $b_{\ell, k}(n)$ modulo $2$ when $ (\ell, k) = (3,8), (4, 7)$, for $b_{\ell, k}(n)$ modulo $8$, modulo $9$ and modulo $12$ when $(\ell, k) = (4, 9)$ and $b_{\ell,...

Let \(B_{l,m}(n)\) denote the number of (l, m)-regular bipartitions of n. Recently, many authors proved several infinite families of congruences modulo 3, 5 and 11 for \(B_{l,m}(n)\). In this paper, we use theta function identities to prove infinite families of congruences modulo m for (l, m)-regular bipartitions, where \(m\in \{7,3,11,13,17\}\).

Let $B_{l,m}(n)$ denote the number of $(l,m)$-regular bipartitions of $n$. Recently, many authors proved several infinite families of congruences modulo $3$, $5$ and $11$ for $B_{l,m}(n)$. In this paper, using theta function identities to prove infinite families of congruences modulo $m$ for $(l,m)$-regular bipartitions, where $m\in\{3,11,13,17\}$.

A partition of $n$ is $l$-regular if none of its parts is divisible by $l$. Let $b_l(n)$ denote the number of $l$-regular partitions of $n$. In this paper, using theta function identities due to Ramanujan, we establish some new infinite families of congruences for $b_l(n)$ modulo $l$, where $l=13,17,23$.

International audience A partition of n is l-regular if none of its parts is divisible by l. Let b l (n) denote the number of l-regular partitions of n. In this paper, using theta function identities due to Ramanujan, we establish some new infinite families of congruences for b l (n) modulo l, where l = 17, 23, and for b 65 (n) modulo 13.

A partition of n is called a t-core partition of n if none of its hook numbers are multiples of t. Let the number of t-core partitions of n be denoted by . Recently, G. E. Andrews defined combinatorial objects which he called singular overpartitions, overpartitions of n in which no part is divisible by k and only parts may be overlined. Let the num...

Let \(B_\ell (n)\) denote the number of \(\ell \)-regular bipartitions of n. In this paper, we prove several infinite families of congruences satisfied by \(B_\ell (n)\) for \(\ell \in {\{5,7,13\}}\). For example, we show that for all \(\alpha >0\) and \(n\ge 0\), $$\begin{aligned} B_5\left( 4^\alpha n+\frac{5\times 4^\alpha -2}{6}\right)\equiv & {...

Recently, Andrews defined combinatorial objects which he called singular overpartitions and proved that these singular overpartitions which depend on two parameters k and i can be enumerated by the function , which denotes the number of overpartitions of n in which no part is divisible by k and only parts may be overlined. G. E. Andrews, S. C. Chen...

In this paper, we establish an interesting q-identity and an integral representation of a q-continued fraction of Ramanujan. We also compute explicit evaluation of this continued fraction and derive its relation with Ramanujan Göllnitz-Gordon continued fraction.