Neville Robbins

collaborators

2 papers

math.NT2014

Partitions with fixed differences between largest and smallest parts

George E. Andrews, Matthias Beck, Neville Robbins

We study the number $p (n, t)$ of partitions of $n$ with difference $t$ between largest and smallest parts. Our main result is an explicit formula for the generating function $P_t(q)…

math.NT2014

Variations on a Generating-Function Theme: Enumerating Compositions with Parts Avoiding an Arithmetic Sequence

Matthias Beck, Neville Robbins

A \Def{composition} of a positive integer $n$ is a $k$ -tuple $(ł_{1}, ł_{2}, \dots, ł_{k}) \in Z_{> 0}^{k}$ such that $n = ł_{1} + ł_{2} + \dots + ł_{k}$ . Our goal is to enumerate those composi…