Sumit Kumar Jha

collaborators

3 papers

math.GM2020

An identity involving number of representations of $n$ as a sum of $r$ triangular numbers

Sumit Kumar Jha

Let $\sum_{d ∣ n}$ denote sum over divisors of a positive integer $n$ , and $t_{r} (n)$ denote the number of representations of $n$ as a sum of $r$ triangular numbers. Then we prove th…

math.GM2020

Formulas for the number of $k$ -colored partitions and the number of plane partitions of $n$ in terms of the Bell polynomials

Sumit Kumar Jha

We derive closed formulas for the number of $k$ -coloured partitions and the number of plane partitions of $n$ in terms of the Bell polynomials.

math.GM2020

A formula for the $r$ -coloured partition function in terms of the sum of divisors function and its inverse

Sumit Kumar Jha

Let $p_{- r} (n)$ denote the $r$ -coloured partition function, and $σ (n) = \sum_{d ∣ n} d$ denote the sum of positive divisors of $n$ . The aim of this note is to prove the following $$ p_{…

An identity involving number of representations of n as a sum of r triangular numbers

Formulas for the number of k-colored partitions and the number of plane partitions of n in terms of the Bell polynomials

A formula for the r-coloured partition function in terms of the sum of divisors function and its inverse

An identity involving number of representations of $n$ as a sum of $r$ triangular numbers

Formulas for the number of $k$ -colored partitions and the number of plane partitions of $n$ in terms of the Bell polynomials

A formula for the $r$ -coloured partition function in terms of the sum of divisors function and its inverse