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master's thesis
Spernerova lema i primjene
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:399316
Pomper, Jurica
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Pomper, J. (2014). Spernerova lema i primjene (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:399316

Pomper, Jurica. "Spernerova lema i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:399316

Pomper, Jurica. "Spernerova lema i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:399316

Pomper, J. (2014). 'Spernerova lema i primjene', Master's thesis, University of Zagreb, Faculty of Science, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:399316

Pomper J. Spernerova lema i primjene [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:217:399316

J. Pomper, "Spernerova lema i primjene", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:399316

Metadata
TitleSpernerova lema i primjene
AuthorJurica Pomper
MentorMatija Kazalicki (mentor)
Committee memberMatija Kazalicki (predsjednik povjerenstva)
Committee memberGoran Muić (član povjerenstva)
Committee memberMarcela Hanzer (član povjerenstva)
Committee memberMladen Jurak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-09-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Njemački matematičar Emmanuel Sperner prvi je dokazao rezultat koji će se kasnije po njemu zvati Spernerova lema, a on kaze da svaka Spernerova triangulacija n-simpleksa sadrži neparan broj potpuno označenih n-simpleksa. U ovom radu navodimo dokaz tog rezultata, kao i njegovu primjenu na probleme pravedne raspodjele torte i stanarine. Osim toga, pokazujemo vezu s Brouwerovim teoremom o fiksnoj točki i na kraju navodimo vezu Brouwerovog teorema s igrom Hex.
Abstract (english)
Emmanuel Sperner, a German mathematician, was the first to prove a result which will later be named after him and known as Sperner’s lemma, which says that every Sperner triangulation of an n-simplex contains an odd number of fully labelled n-simplexes. We present the proof of that result and apply it on fair division problems, namely on cake cutting and rental division. Besides that we show the connection with the Brouwer’s fixed point theorem and in the end the connection between the Brouwer’s theorem and the game of Hex.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:399316
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-01-30 10:27:20