Combinatorics

This is the report on the Oberwolfach workshop on Combinatorics, held 1–7 January 2006. Combinatorics is a branch of mathematics studying families of mainly, but not exclusively, finite or countable structures – discrete objects. The discrete objects considered in the workshop were graphs, set systems, discrete geometries, and matrices. The programme consisted of 15 invited lectures, 18 contributed talks, and a problem session focusing on recent developments in graph theory, coding theory, discrete geometry, extremal combinatorics, Ramsey theory, theoretical computer science, and probabilistic combinatorics

On valences of polyhedra

AbstractThe paper deals with the problem of realizing polyhedral maps by polyhedra. Here, a polyhedral map is a two-dimensional cell-complex whose underlying point set is a closed topological manifold in some finite dimensional real space Rd and a polyhedron is a polyhedral map with the property that the two-dimensional cells are convex polygons. A polyhedron realizes a polyhedral map if the corresponding cell complexes are isomorphic. The central problem is to characterize those polyhedral maps which can be realized by polyhedra. The present paper gives necessary combinatorial conditions and states various unsolved problems

On valences of polyhedra

SIGLETIB: RO 7722(221) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman