Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem by David E. Handelman

Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem

byDavid E. Handelman

Paperback | October 7, 1987

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Emanating from the theory of C*-algebras and actions of tori theoren, the problems discussed here are outgrowths of random walk problems on lattices. An AGL (d,Z)-invariant (which is a partially ordered commutative algebra) is obtained for lattice polytopes (compact convex polytopes in Euclidean space whose vertices lie in Zd), and certain algebraic properties of the algebra are related to geometric properties of the polytope. There are also strong connections with convex analysis, Choquet theory, and reflection groups. This book serves as both an introduction to and a research monograph on the many interconnections between these topics, that arise out of questions of the following type: Let f be a (Laurent) polynomial in several real variables, and let P be a (Laurent) polynomial with only positive coefficients; decide under what circumstances there exists an integer n such that Pnf itself also has only positive coefficients. It is intended to reach and be of interest to a general mathematical audience as well as specialists in the areas mentioned.
Title:Positive Polynomials, Convex Integral Polytopes, and a Random Walk ProblemFormat:PaperbackProduct dimensions:147 pages, 9.25 X 6.1 X 0 inShipping dimensions:147 pages, 9.25 X 6.1 X 0 inPublished:October 7, 1987Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540184007

ISBN - 13:9783540184003

Appropriate for ages: All ages

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Table of Contents

Definitions and notation.- A random walk problem.- Integral closure and cohen-macauleyness.- Projective RK-modules are free.- States on ideals.- Factoriality and integral simplicity.- Meet-irreducibile ideals in RK.- Isomorphisms.