Topological Methods in Nonlinear Analysis

Combinatorial lemmas for oriented complexes

Adam Idzik and Konstanty Junosza-Szaniawski

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Abstract

A solid combinatorial theory is presented. The generalized Sperner lemma for chains is derived from the combinatorial Stokes formula. Many other generalizations follow from applications of an $n$-index of a labelling defined on chains with values in primoids. Primoids appear as the most general structure for which Sperner type theorems can be formulated. Their properties and various examples are given. New combinatorial theorems for primoids are proved. Applying them to different primoids the well-known classic results of Sperner, Fan, Shapley, Lee and Shih are obtained.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 32, Number 2 (2008), 379-409.

Dates
First available in Project Euclid: 13 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1463151171

Mathematical Reviews number (MathSciNet)
MR2494062

Zentralblatt MATH identifier
1176.05019

Citation

Idzik, Adam; Junosza-Szaniawski, Konstanty. Combinatorial lemmas for oriented complexes. Topol. Methods Nonlinear Anal. 32 (2008), no. 2, 379--409. https://projecteuclid.org/euclid.tmna/1463151171


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