The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.

The basic ideas of the subject and the analogues with enumerative combinatorics are described and exploited.
Reviews
'Geometers and combinatorialists will find this a stimulating and fruitful tale.' Fachinformationszentrum Karlsruhe
' ... a brief and useful introduction ...' European Mathematical Society



Book Information
ISBN 9780521593625
Author Daniel A. Klain
Format Hardback
Page Count 196
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 400g
Dimensions(mm) 216mm * 140mm * 14mm