4 papers
The Partition Pairing Theorems I
George Andrews, Manosij Ghosh Dastidar
The aim of this paper is to introduce pairing theory for partitions. We begin with two statistics on integer partitions, the \emph{pairing index} and the \emph{pairing rank}. The p…
Sign Laws and Mock Theta Functions
Manosij Ghosh Dastidar
Let \[ ρ(q)=\sum_{m\geq 0}\frac{q^{2m(m+1)}}{(1+q+q^2)(1+q^3+q^6)\cdots(1+q^{2m+1}+q^{4m+2})} =\sum_{n\geq 0}r(n)q^n \] be Ramanujan's third order mock theta function. We prove the…
Sign law for Ramanujan's third order mock theta function
Manosij Ghosh Dastidar
We study the coefficients of Ramanujan's third order mock theta function \[ ρ(q)=\sum_{m\geq 0} \frac{q^{2m(m+1)}}{(1+q+q^2)(1+q^3+q^6)\cdots(1+q^{2m+1}+q^{4m+2})} =\sum_{n\geq 0}r…
Some congruences modulo 5 and 25 for overpartition
Shane Chern, Manosij Ghosh Dastidar
We present two new Ramanujan-type congruences modulo 5 for overpartition. We also give an affirmative answer to a conjecture of Dou and Lin, which includes four congruences modulo…