Nyhet

From Christoffel Words to Markoff Numbers

AvChristophe Reutenauer

Inbunden, Engelska, 2026

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Beskrivning

In 1875, Elwin Bruno Christoffel introduced a special class of words on a binary alphabet linked to continued fractions which would go on to be known as Christoffel words. Some years later, Andrey Markoff published his famous theory, now called the Markoff theory. Markoff's theory characterized certain quadratic forms and real numbers by extremal inequalities. Both classes are constructed using certain natural numbers, known as Markoff numbers, and they form part of a solution to the Markoff Diophantine equation. More basically, they are constructed using certain words, essentially Christoffel words.The link between Christoffel words and Markoff's theory was noted by Ferdinand Frobenius in 1913, but has been neglected in recent times. Motivated by this overlooked connection, this book looks to expand on the relationship between these two areas. The first part of the book focuses on the classical theory of Markoff, while Part II explores the more advanced and recent results of the theory of Christoffel words. This new edition includes many additional exercises and solutions, as well as expanded sections on quadratic forms and quadratic numbers, two new chapters on standard words and the commutator subgroup, and revised results in combinatorics on words.

Produktinformation

Utgivningsdatum:2026-07-23
Mått:160 x 240 x 20 mm
Vikt:591 g
Format:Inbunden
Språk:Engelska
Antal sidor:272
Upplaga:2
Förlag:OUP OXFORD
ISBN:9780197907559

Utforska kategorier

Diskret matematik inom Naturvetenskap och teknik
Talteori inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Mer om författaren

Christophe Reutenauer was educated at École Normale Supérieure in Paris, and subsequently undertook his postgraduate studies at the Université de Paris 6 in 1977, before going on to complete his doctorate thesis at the same institution in 1980. He was a former researcher at the CNRS (Centre National de la Recherche Scientifique) in Paris, and LITP (Laboratoire d'Informatique Théorique et de Programmation) from 1976 to 1990. Reutenauer has been a professor at UQAM (Université du Québec à Montréal) since 1985, and was also a professor at the University of Strasbourg between 1999 and 2001. Since then, he has been an invited professor or researcher at several universities, including Saarbrücken, Darmstadt, Roma, Napoli, Palermo, UQAM, San Diego (UCSD), Strasbourg, Montpelier, Bordeaux, Paris-Est, Nice, and the Mittag-Leffler Institute. He was also the Canadian Research Chair for Algebra, Combinatorics and mathematical Informatics between 2001 and 2015.

Recensioner i media

Review from previous edition For the first time in literature on the subject, this textbook treats the two aspects of Markoff's Theory simultaneously. Numerous figures throughout the book help to illustrate its points and provide proofs of discrete geometry.

Innehållsförteckning

Part I The theory of Markoff 1: Basics 2: Words 3: Markoff numbers 4: The Markoff property 5: Continued fractions 6: Binary quadratic forms 7: Lagrange number 8: Words and quadratic numbers 9: Lagrange numbers less than three 10: Markoff's theorem for approximations 11: Markoff's theorem for quadratic forms 12: Numerology 13: Historical notes Part II The theory of Christoffel words 14: Palindromes and periods 15: Conjugates and factors 16: Standard words 17: Lyndon words and Christoffel words 18: Sturmian words 19: Stern-Brocot tree 20: Free group on two generators 21: The commutator subgroup SL2(Z)'