Ein operativer Beweis des Spernerschen Lemmas (Q796534)

The authors give a proof of Sperner's lemma being more transparent than the well-known proofs. Coming from any simplicial partition \(\Sigma\) of an affine simplex \(T=(p_ 0,p_ 1,...,p_ n) (n\in {\mathbb{N}}_ 0)\) they at first determine an admissable valuation of the vertices of \(\Sigma\) with exactly one n-dimensional partial simplex being completely denominated. They finish the proof by showing that the number of the partial simplex of \(\Sigma\) being completely denominated always changes by an even number if the valuation of a vertex of \(\Sigma\) has been changed admissably.