Jorge Luis Ramírez Alfonsín
Maître de Conférences
Office 1E4 (1st floor, wing E) 175, rue du Chevaleret 75013 Paris (How to get there ?) Mail Université Pierre et Marie Curie (Paris 6) address Combinatoire et Optimisation - case 189 4, place Jussieu 75252 Paris Cedex 05, France Telephone 01 44 27 85 37 Fax 01 44 27 27 24 e-mail ramirez@math.jussieu.fr

Version française

• Discrete and Convex Geometry


I am interested in problems related with matroids and oriented matroids, particularly those in connection with arrangements of hyperplanes and polytopes.

• Elementary Number theory


I work on the following problem, known as the diophantine Frobenius problem:

given relatively prime positive integers, find the largest integer which cannot be written as a nonnegative integer linear combination of them.

The article How hard can it be? is a popular work about the Frobenius problem (translation in German here )

• Knot Theory
  
  

I am interested in the following question: what is the smallest positive integer n, such that every set of n points in general position in the space generate a knot of a given type?

• Graph Theory


I am interested in decompostions of the complete graphs into certain structures like cycles and trees (decompositions closely related to graceful labelings).

• D. Labrousse and J.L. Ramírez Alfonsín, A tiling problem and the Frobenius number, Contribution to M. Nathanson Fetschrift ( pdf, ps )

• V. Chatelain and J.L. Ramírez Alfonsín, Matroid base polytope decomposition, submitted ( pdf )

• Mathématiques discrètes

• Arithmétique

• Graphes et Combinatoire

• Matroïdes et applications

• Approche constructive de l'optimisation