Planar automaton accepting Le-diagram, alternative tableaux

The structure of alternative tableaux

In this paper we study alternative tableaux introduced by Viennot [17]. These tableaux are in simple bijection with permutation tableaux, dened previously by Postnikov [12]. We exhibit a simple recursive structure for alternative tableaux. From this decomposition, we can easily deduce a number of enumerative results. We also give bijections between these tableaux and certain classes of labeled ...

Hierarchical planar voronoi diagram approximations

Generalized Dumont-foata Polynomials and Alternative Tableaux

Dumont and Foata introduced in 1976 a three-variable symmetric refinement of Genocchi numbers, which satisfies a simple recurrence relation. A six-variable generalization with many similar properties was later considered by Dumont. They generalize a lot of known integer sequences, and their ordinary generating function can be expanded as a Jacobi continued fraction. We give here a new combinato...

The Voronoi Diagram of Planar Convex Objects

This paper presents a dynamic algorithm for the construction of the Euclidean Voronoi diagram of a set of convex objects in the plane. We consider first the Voronoi diagram of smooth convex objects forming pseudocircles set. A pseudo-circles set is a set of bounded objects such that the boundaries of any two objects intersect at most twice. Our algorithm is a randomized dynamic algorithm. It do...

Planar decompositions of tableaux and Schur function determinants

In this paper we describe planar decompositions of skew shape tableaux into strips and use the shapes of these strips to generate a determinant. We then prove that each of these determinants is equal to the Schur function for the skew shape. The Jacobi-Trudi identity, the dual Jacobi-Trudi identity, the Giambelli identity and the rim ribbon identity of Laseoux and Pragacz are all special cases ...