Combinatorial Convexity

Häftad, Engelska, 2022

849 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

This book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Caratheodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Caratheodory, and the $(p, q)$ theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory.The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.

Produktinformation

Utgivningsdatum2022-02-28
Mått178 x 254 x undefined mm
Vikt294 g
FormatHäftad
SpråkEngelska
SerieUniversity Lecture Series
Antal sidor148
FörlagAmerican Mathematical Society
ISBN9781470467098

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik

Basic conceptsCaratheodory's theoremRadon's theoremTopological RadonTverberg's theoremGeneral positionHelly's theoremApplications of Helly's theoremFractional HellyColourful CaratheodoryColourful Caratheodory againColourful HellyTverberg's theorem againColourful Tverberg theoremSarkaria and Kirchberger generalizedThe Erdos-Szekers theoremThe same type lemmaBetter bound for the Erdos-Szekeres numberCovering number, planar caseThe stretched gridCovering number, general caseUpper bound on the covering numberThe point selection theoremHomogeneous selectionMissing few simplicesWeak $\varepsilon$-netsLower bound on the size of weak $\varepsilon$-netsThe $(p,q)$ theoremThe colourful $(p,q)$ theorem$d$-intervalsHalving lines, havling planesConvex lattice setsFractional Helly for convex lattice setsBibliographyIndex