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From Christoffel Words to Markoff Numbers

From Christoffel Words To Markoff Numbers


In 1875, Elwin Bruno Christoffel introduced a special class of words on a binary alphabet linked to continued fractions which would go onto be known as Christoffel words. Some years later, Andrey Markoff published his famous theory, the now called Markoff theory. It characterized certain quadratic forms and certain real numbers by extremal inequalities. Both classes are constructed using certain natural numbers - known as Markoff numbers - and they are characterized by a certain Diophantine equality. More basically, they are constructed using certain words - essentially the Christoffel words. The link between Christoffel words and the theory of Markoff 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. Part 1 focuses on the classical theory of Markoff, while Part II explores the more advanced and recent results of the theory of Christoffel words.



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    Conditions Guide
  • Format: Hardcover
  • Sold by: --
  • Language: English
  • Publisher: Oxford Univ Pr
  • ISBN-13: 9780198827542
  • ISBN: 0198827547
  • Publication Year: 2019
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HPB condition ratings
  • New: Item is brand new, unused and unmarked, in flawless condition.
  • Fine/Like New (F): No defects, little usage. May show remainder marks. Older books may show minor flaws.
  • Very Good (VG): Shows some signs of wear and is no longer fresh. Attractive. Used textbooks do not come with supplemental materials.
  • Good (G): Average used book with all pages present. Possible loose bindings, highlighting, cocked spine or torn dust jackets. Used textbooks do not come with supplemental materials.
  • Fair (FR): Obviously well-worn, but no text pages missing. May be without endpapers or title page. Markings do not interfere with readability. Used textbooks do not come with supplemental materials.
  • Poor (P): All text is legible but may be soiled and have binding defects. Reading copies and binding copies fall into this category. Used textbooks do not come with supplemental materials.
Conditions Guide
HPB condition ratings
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