1028023197  

Forbidden configurations in discrete geometry / David Eppstein

Englisch

Cambridge : Cambridge University Press, [2018]

1 Online-Ressource (ix, 230 Seiten)

Erscheint auch als: Druck-Ausgabe- Eppstein, David *1963-*: Forbidden configurations in discrete geometry. - Cambridge, United Kingdom : Cambridge University Press, 2018. - ix, 230 Seiten

978-1-108-53918-0 : ebook

Weitere Ausgaben: 978-1-108-42391-5 (Druckausgabe) : hardback, 978-1-108-43913-8 (andere physische Form) : paperback

DOI: 10.1017/9781108539180

*Diskrete Geometrie / Planarer Graph / Konfiguration

*Combinatorial analysis ; Discrete geometry

*Discrete geometry ; Combinatorial analysis

Klassifikation der Library of Congress: QA640.7

Dewey Dezimal-Klassifikation: 516/.11;

Mathematics Subject Classification: *52-02

Mathematics Subject Classification: 52C10

Mathematics Subject Classification: 05B30

Mathematics Subject Classification: 52B55

This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets

https://zbmath.org/?q=an:1417.52001 [Zentralblatt MATH]

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