Combinatorial lemmas for oriented complexes
Keywords
Labelling, primoid, pseudomanifold, Sperner lemma, combinatorial Stokes formulaAbstract
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.Downloads
Published
2008-12-01
How to Cite
1.
IDZIK, Adam and JUNOSZA-SZANIAWSKI, Konstanty. Combinatorial lemmas for oriented complexes. Topological Methods in Nonlinear Analysis. Online. 1 December 2008. Vol. 32, no. 2, pp. 379 - 409. [Accessed 29 March 2024].
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