The morphology of infinite tournaments. Application to the growth of their profile
| dc.creator | Boudabbous, Youssef | |
| dc.creator | Pouzet, Maurice | |
| dc.date | 2008-01-26 | |
| dc.date.accessioned | 2026-07-07T08:56:42Z | |
| dc.date.available | 2026-07-07T08:56:42Z | |
| dc.description | A tournament is \emph{acyclically indecomposable} if no acyclic autonomous set of vertices has more than one element. We identify twelve infinite acyclically indecomposable tournaments and prove that every infinite acyclically indecomposable tournament contains a subtournament isomorphic to one of these tournaments. The {\it profile} of a tournament $T$ is the function $ϕ_T$ which counts for each integer $n$ the number $ϕ_T(n)$ of tournaments induced by $T$ on the $n$-element subsets of $T$, isomorphic tournaments being identified. As a corollary of the result above we deduce that the growth of $ϕ_T$ is either polynomial, in which case $ϕ_T(n)\simeq an^k$, for some positive real $a$, some non-negative integer $k$, or as fast as some exponential. | |
| dc.description | 25 pages, presented at CGCS 2007(Luminy, France, May 2-4 2007) in honor of Michel Deza | |
| dc.identifier | https://arxiv.org/abs/0801.4069 | |
| dc.identifier | http://arxiv.org/abs/0801.4069 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146706 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A16, 05C20 | |
| dc.title | The morphology of infinite tournaments. Application to the growth of their profile | |
| dc.type | text |