Discrete mathematics

Tournament

Set (abstract data type)

Computer science

Mathematics

Object (grammar)

Artificial intelligence

Geometry

Combinatorics

Point (geometry)

Programming language

Line (geometry)

Joins

Canadian Mathematical Bulletin

Given a set of n points, with each pair of distinct points joined by a line that is oriented towards exactly one of the points, then the resulting configuration is called a (roun-drobin) tournament. A tournament is reducible if the points can be separated into two non-empty subsets, A and B, such that every line that joins a point in A to a point in B is oriented towards the point in B. If a tournament is not reducible it is called irreducible. The object of this note is to derive an approximation for P(n), the probability that a tournament on n point, chosen at random from the set of possible ones, will be irreducible. p(1)=1, by definition.

Almost all Tournaments are Irreducible