On a Balanced Property of Compositions
| dc.creator | Bona, Miklos | |
| dc.date | 2006-09-29 | |
| dc.date.accessioned | 2026-07-07T07:25:27Z | |
| dc.date.available | 2026-07-07T07:25:27Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0609845 | |
| dc.identifier | http://arxiv.org/abs/math/0609845 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116720 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A16 | |
| dc.title | On a Balanced Property of Compositions | |
| dc.type | text |