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...

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...

The purpose of this paper is to compute the Banzhaf power index for weighted voting games as well as weighted double and triple majority games. We calculate the Banzhaf index in an exact way by generating functions, with a signi...cant decrease of the computational complexity. Moreover, the Banzhaf indices are calculated for the decision rules approved in the Nice summit meeting, which will be ...

1.1. Classical r-matrices. In the early eighties, Belavin and Drinfeld [BD] classified nonskewsymmetric classical r-matrices for simple Lie algebras. It turned out that such r-matrices, up to isomorphism and twisting by elements from the exterior square of the Cartan subalgebra, are classified by combinatorial objects which are now called Belavin-Drinfeld triples. By definition, a Belavin-Drinf...

Recent results on sparse coding and independent component analysis suggest that human vision first represents a visual image by a linear superposition of a relatively small number of localized, elongate, oriented image bases. With this representation, the sketch of an image consists of the locations, orientations, and elongations of the image bases, and the sketch can be visually illustrated by...