Simple neighbourhoods in triple systems

Leaves, excesses and neighbourhoods in triple systems

Alternating triple systems with simple Lie algebras of derivations

We prove a formula for the multiplicity of the irreducible representation V (n) of sl(2, C) as a direct summand of its own exterior cube ΛV (n). From this we determine that V (n) occurs exactly once as a summand of ΛV (n) if and only if n = 3, 5, 6, 7, 8, 10. These representations admit a unique sl(2)-invariant alternating ternary structure obtained from the projection ΛV (n) → V (n). We calcul...

On the Chromatic Number of Simple Triangle-Free Triple Systems

A hypergraph is simple if every two edges share at most one vertex. It is trianglefree if in addition every three pairwise intersecting edges have a vertex in common. We prove that there is an absolute constant c such that the chromatic number of a simple triangle-free triple system with maximum degree ∆ is at most c √ ∆/ log ∆. This extends a result of Johansson about graphs, and is sharp apar...

Cyclic, Simple and Indecomposable Three-Fold Triple Systems

In 2000, Rees and Shalaby constructed simple indecomposable two-fold cyclic triplesystems for all v ≡ 0, 1, 3, 4, 7, and 9 (mod 12) where v = 4 or v ≥ 12, using Skolem-type sequences.We construct, using Skolem-type sequences, three-fold triple systems having theproperties of being cyclic, simple, and indecomposable for all admissible orders v, withsome possible exception...

Concept Neighbourhoods in Knowledge Organisation Systems

This paper discusses the application of concept neighbourhoods (in the sense of Formal Concept Analysis) to Knowledge Organisation Systems. Examples are provided using Roget’s Thesaurus, WordNet and Wikipedia cat-