The Borsuk-Ulam Theorem in Combinatorics

Title

The Borsuk-Ulam Theorem in Combinatorics

 Author

Jaspers, Ilja (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Delft Institute of Applied Mathematics)

Contributor

Gijswijt, Dion (mentor)
Hart, Klaas Pieter (graduation committee)
Spandaw, Jeroen (graduation committee)

Degree granting institution

Delft University of Technology

 Date

2017-08-23

 Abstract

We examine and prove the Borsuk-Ulam theorem and its combinatorial equivalent Fan's lemma. The theory of simplicial complexes and triangulations plays an important role in this. The Borsuk-Ulam theorem and Fan's lemma will be used to provide proofs for the Brouwer fixed point theorem and the combinatorial Sperner's lemma. Lastly the Borsuk-Ulam theorem will be applied in determining the chromatic number of Kneser graphs.

 Subject

borsuk-ulam
fan's lemma
combinatorics
brouwer fixed point
sperner's lemma
kneser graph
chromatic number
simplicial complex
triangulation

 To reference this document use:

http://resolver.tudelft.nl/uuid:ff91453c-455c-4a67-bc38-f8d8e6eb223c

 Part of collection

Student theses

 Document type

bachelor thesis

 Rights

© 2017 Ilja Jaspers
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PDF Ilja_Jaspers_The_Borsuk_U ... torics.pdf 339.56 KB
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