3 papers
math.CO2026
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…
math.NT2026
Sign Laws and Mock Theta Functions
Manosij Ghosh Dastidar
Let \[ Ï(q)=\sum_{m\geq 0}\frac{q^{2m(m+1)}}{(1+q+q^2)(1+q^3+q^6)\cdots(1+q^{2m+1}+q^{4m+2})} =\sum_{n\geq 0}r(n)q^n \] be Ramanujan's third order mock theta function. We prove th…
math.NT2026
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 \[ Ï(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}…