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COMBINATORICS

2002

9 years 10 months ago
2002

If we compose sufficiently many random functions on a finite set, then the composite function will be constant. We determine the number of compositions that are needed, on average...

COMBINATORICS

2002

9 years 10 months ago
2002

In 1906 Axel Thue showed how to construct an infinite non-repetitive (or squarefree) word on an alphabet of size 3. Since then this result has been rediscovered many times and ext...

COMBINATORICS

2002

9 years 10 months ago
2002

A map is a graph equipped with a circular order of edges around each vertex. These circular orders represent local planar embeddings. The genus of a map is the minimal genus of an...

COMBINATORICS

2002

9 years 10 months ago
2002

The n-th Heilbronn number, Hn, is the largest value such that n points can be placed in the unit square in such a way that all possible triangles defined by any three of the point...

COMBINATORICS

2002

9 years 10 months ago
2002

A sink-free orientation of a finite undirected graph is a choice of orientation

COMBINATORICS

2002

9 years 10 months ago
2002

We obtain a characterization of (321, 3

COMBINATORICS

2002

9 years 10 months ago
2002

Let G = (V, E) be a connected undirected graph and S a subset of vertices. If for all vertices v V , the sets Br(v) S are all nonempty and different, where Br(v) denotes the set...

COMBINATORICS

2002

9 years 10 months ago
2002

An efficient and purely combinatorial algorithm for calculating products in arbitrary Coxeter groups is presented, which combines ideas of Fokko du Cloux and myself. Proofs are lar...

COMBINATORICS

2002

9 years 10 months ago
2002

The lattice of noncrossing partitions can be embedded into the Cayley graph of the symmetric group. This allows us to rederive connections between noncrossing partitions and parki...

COMBINATORICS

2002

9 years 10 months ago
2002