A combinatorial lemma and its applications

Piotr Maćkowiak

Abstract

In this paper, we present a generalization of a combinatorial lemma we stated and proved in a recent work. Then we apply the generalized lemma to prove: (1) a theorem on the existence of a zero for an excess demand mapping, (2) the existence of a continuum of zeros for a parameterized excess demand mapping, (3) Sperner’s lemma on labelings of triangulations. Proofs of these results are constructive: they contain algorithms (based on the combinatorial lemma) for the computation of objects of interest or, at least, of their approximations.
Author Piotr Maćkowiak (WIiGE / KEM)
Piotr Maćkowiak,,
- Department of Mathematical Economics
Journal seriesJournal of Inequalities and Applications, ISSN 1029-242X, [1025-5834], (A 30 pkt)
Issue year2016
No105
Pages1-22
Publication size in sheets1.05
Keywords in EnglishBrowder fixed point theorem, combinatorial methods, continuum of zeros, equilibrium, fixed point, Kakutani fixed point theorem, Sperner lemma, zero of a map
ASJC Classification2603 Analysis; 2604 Applied Mathematics; 2607 Discrete Mathematics and Combinatorics
DOIDOI:10.1186/s13660-016-1043-y
URL https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-016-1043-y
Languageen angielski
Score (nominal)30
Score sourcejournalList
ScoreMinisterial score = 20.0, 16-12-2019, ArticleFromJournal
Ministerial score (2013-2016) = 30.0, 16-12-2019, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.733; WoS Impact Factor: 2016 = 0.791 (2) - 2016=0.82 (5)
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