Combinatorial analogs of Brouwer's fixed-point theorem on a bounded polyhedron
This paper presents a combinatorial theorem (Theorem 1) on a bounded polyhedron for an unrestricted labelling of a triangulation of the polyhedron, which can be interpreted as an extension of the generalized Sperner lemma. When the labelling function is dual-proper, this theorem specializes to a second combinatorial theorem on the polyhedron, that is an extension of Scarf's dual Sperner lemma. These results are shown to be analogs of Brouwer's fixed-point theorem on a polyhedron, and are also shown to generalize other combinatorial theorems on bounded polyhedra. As part of the combinatorial proof of theorem 1, a pseudomanifold construction for a polyhedron and its dual are also presented.
scientific article; zbMATH DE number 4192641
scientific article