On the polynomial representation for the number of partitions with fixed length
On the polynomial representation for the number of partitions with fixed length
In this paper, it is shown that the number $M(n,k)$ of partitions of a nonnegative integer $n$ with $k$ parts can be described by a set of $\widetilde {k}$ polynomials of degree $k-1$ in $Q_{\widetilde {k}}$, where $\widetilde {k}$ denotes the least common multiple of the $k$ integers $1, 2, …