Der kombinatorische Kern des Spernerschen Lemmas; eine Beweisanalyse (Q796535)

By analysing the operative proof of \textit{R. Struve} and \textit{E. Wittmann} [ibid. 31, 134-141 (1984; reviewed above)] the author develops the concept of the n-dimensional simplicial design (\(n\in {\mathbb{N}})\) in analogy to the t-design. With the help of the n-dimensional simplicial plan be succeeds in proving Sperner's lemma in a very transparent way. Applying to this an n-dimensional simplicial design is meant to be an ordered pair (P,B) with P being a finite set and B being a nonempty set of subsets of P with \(n+1\) elements fulfilling special properties.