Farey Sequences

As a first comprehensive overview on Farey sequences and subsequences, this monograph is intended as a reference for anyone looking for specific material or formulas related to the subject. Duality of subsequences and maps between them are discussed and explicit proofs are shown in detail.

From the Content
Basic structural and enumerative properties of Farey sequences, Collective decision making, Committee methods in pattern recognition, Farey duality, Farey sequence, Fundamental Farey subsequences, Monotone bijections between Farey subsequences

• The first book devoted entirely to the Farey sequence, an attractive and popular construct in number theory
• A very detailed and readily accessible reference text on basic structural and enumerative properties of the Farey sequence

"In the words of the author, this book “is intended as a detailed exposition of the basic properties of Farey (sub)sequences, and as a handbook of formulas”. As such, the reader should not expect a traditional textbook, but rather an exhaustive reference work, concentrating on a short list of related properties, which are studied in detail for each of the sequences under consideration. Proofs of the main results are provided. These, due to the nature of the subject, only require a basic familiarity with elementary number theory, but the devil is in the details, and those studying the subject and wanting to verify a particular formula will need to carefully review the numerous cases for themselves. [...]All in all, this book should provide a useful reference for anyone working with Farey fractions and, in particular, wanting quick access to extensive lists and tables of explicit formulas [...]"
Luis Manuel Navas Vicente in: Mathematical Reviews Clippings MR3752136 (2018)

"This book discusses in meticulous detail the structure and properties of the standard Farey sequence and subsequences. They have a rich structure with combinatorial and number-theoretic properties."
Balasubramanian Sury in: Zentralblatt MATH 1396.11002 (2018)