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Markov's theorem and 100 years of the uniqueness conjecture : a mathematical journey from irrational numbers to perfect matchings

Author: Martin Aigner
Publisher: Cham ; New York : Springer, ©2013.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov's theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov's theorem.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Aigner, Martin, 1942-
Markov's theorem and 100 years of the uniqueness conjecture.
Cham : Springer, [2013]
(DLC) 2013944221
(OCoLC)859584220
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Martin Aigner
ISBN: 9783319008882 3319008889
OCLC Number: 853659945
Description: 1 online resource (x, 257 pages) : illustrations
Contents: Part I. Numbers --
1. Approximation of irrational numbers --
2. Markov's theorem and the uniqueness conjecture --
Part II. Trees --
3. The Markov tree --
4. The Cohn tree --
Part III. Groups --
5. The modular group --
6. The free group F2 --
Part IV. Words --
7. Christoffel words --
8. Sturmian words --
Part V. Finale --
9. Proof of Markov's theorem --
10. The uniqueness conjecture.
Responsibility: Martin Aigner.

Abstract:

This book takes the reader on a mathematical journey from the number-theoretic setting of the Theorem of Markov and its Uniqueness Conjecture, gradually unfolding many beautiful connections, until in  Read more...

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