Séminaire Gaston Darboux :

Le 13 décembre 2013 à 11:15 - salle 431

Présentée par Chepoi Victor - Université de Marseille

Geometry and combinatorics of lopsided sets

Lopsided sets introduced by Jim Lawrence in 1983 can be regarded as isometric subgraphs of hypercubes for which the intersections with any faces yield isometric subgraphs. They generalize median graphs, alias $1$-skeletons of CAT$(0)$ cube complexes, convex geometries, and intersection patterns of convex sets with orthants. In this talk, we will present several combinatorial and geometric characterizations of lopsided sets. In particular, we present how lopsided sets can be characterized via two associated simplicial complexes and by associated cubical complexes. Joint work with H.-J. Bandelt, A. Dress, J. Koolen.