Combinatorial formulae for multiple set-valued labellings
type: Item
instance of: scholarly article
title: Combinatorial formulae for multiple set-valued labellings
zbMATH Open document ID: 0791.05007
DOI: 10.1007/BF01445093
author: V. Pereyra
published in: Mathematische Annalen
publication date: 1994-04-26T00:00:00Z
full work available at URL: https://eudml.org/doc/165073
review text: We develope the geometric notions of general position maps, \(\pi\)- balanced and \(\pi\)-subbalanced sets and then apply them to prove two general combinatorial formulae for multiple set-valued labellings on simplices related to the celebrated Sperner combinatorial lemma [Abh. Math. Semin. Univ. Hamb. 6, 265-272 (1928; JFM 54.0614.01)]. We apply one of the combinatorial formulae to covering theory of simplices and obtain a new covering theorem which is a common generalization of the Shapley theorem and the Gale theorem.
Mathematics Subject Classification ID: 05A99
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 57Q65
Mathematics Subject Classification ID: 05D05
zbMATH DE Number: 537285
zbMATH Keywords: position maps
zbMATH Keywords: multiple set-valued labellings
zbMATH Keywords: Sperner combinatorial lemma
zbMATH Keywords: covering theorem
zbMATH Keywords: Shapley theorem
zbMATH Keywords: Gale theorem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 537285