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On a Balanced Property of Compositions by Bona, Miklos is a scholarly article available to read on EtoBox.

What is On a Balanced Property of Compositions about?

Let $S$ be a finite set of positive integers with largest element $m$. Let us randomly select a composition $a$ of the integer $n$ with parts in $S$, and let $m(a)$ be the multiplicity of $m$ as a part of $a$. Let $0\leq r<q$ be integers, with $q\geq 2$, and let $p_{n,r}$ be the probability that $m(a)$ is congruent to $r$ modulo $q$. We show that if $S$ satisfies a certain simple condition, then $\lim_{n\to \infty} p_{n,r} =1/q$. In fact, we show that an obvious necessary condition on $S$ turns out to be sufficient.

Author

Bona, Miklos

Published

2006

Language

EN