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.
Rezensionen / Stimmen
'Geometers and combinatorialists will find this a stimulating and fruitful tale.' Fachinformationszentrum Karlsruhe ' ... a brief and useful introduction ...' European Mathematical Society
Reihe
Sprache
Verlagsort
Zielgruppe
Illustrationen
1 Tables, unspecified; 5 Line drawings, unspecified
Maße
Höhe: 222 mm
Breite: 145 mm
Dicke: 14 mm
Gewicht
ISBN-13
978-0-521-59362-5 (9780521593625)
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Schweitzer Klassifikation
Autor*in
Georgia Institute of Technology
Massachusetts Institute of Technology
Introduction; 1. The Buffon needle problem; 2. Valuation and integral; 3. A discrete lattice; 4. The intrinsic volumes for parallelotopes; 5. The lattice of polyconvex sets; 6. Invariant measures on Grassmannians; 7. The intrinsic volumes for polyconvex sets; 8. A characterization theorem for volume; 9. Hadwiger's characterization theorem; 10. Kinematic formulas for polyconvex sets; 11. Polyconvex sets in the sphere; References; Index of symbols; Index.
