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Integer Points in Polyhedra
 
Alexander Barvinok University of Michigan, Ann Arbor, MI
A publication of European Mathematical Society
Front Cover for Integer Points in Polyhedra
Available Formats:
Softcover ISBN: 978-3-03719-052-4
Product Code: EMSZLEC/9
List Price: $44.00
AMS Member Price: $35.20
Please note AMS points can not be used for this product
Front Cover for Integer Points in Polyhedra
Click above image for expanded view
Integer Points in Polyhedra
Alexander Barvinok University of Michigan, Ann Arbor, MI
A publication of European Mathematical Society
Available Formats:
Softcover ISBN:  978-3-03719-052-4
Product Code:  EMSZLEC/9
List Price: $44.00
AMS Member Price: $35.20
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Zurich Lectures in Advanced Mathematics
    Volume: 92008; 200 pp
    MSC: Primary 52; 05; 11;

    This is a self-contained exposition of several core aspects of the theory of rational polyhedra with a view towards algorithmic applications to efficient counting of integer points, a problem arising in many areas of pure and applied mathematics. The approach is based on the consistent development and application of the apparatus of generating functions and the algebra of polyhedra. Topics range from classical, such as the Euler characteristic, continued fractions, Ehrhart polynomial, Minkowski Convex Body Theorem, and the Lenstra–Lenstra–Lovász lattice reduction algorithm, to recent advances such as the Berline–Vergne local formula.

    The text is intended for graduate students and researchers. Prerequisites are a modest background in linear algebra and analysis as well as some general mathematical maturity. Numerous figures, exercises of varying degree of difficulty as well as references to the literature and publicly available software make the text suitable for a graduate course.

    Readership

    Graduate students and research mathematicians interested in geometry and topology.

  • Requests
     
     
    Review Copy – for reviewers who would like to review an AMS book
    Accessibility – to request an alternate format of an AMS title
Volume: 92008; 200 pp
MSC: Primary 52; 05; 11;

This is a self-contained exposition of several core aspects of the theory of rational polyhedra with a view towards algorithmic applications to efficient counting of integer points, a problem arising in many areas of pure and applied mathematics. The approach is based on the consistent development and application of the apparatus of generating functions and the algebra of polyhedra. Topics range from classical, such as the Euler characteristic, continued fractions, Ehrhart polynomial, Minkowski Convex Body Theorem, and the Lenstra–Lenstra–Lovász lattice reduction algorithm, to recent advances such as the Berline–Vergne local formula.

The text is intended for graduate students and researchers. Prerequisites are a modest background in linear algebra and analysis as well as some general mathematical maturity. Numerous figures, exercises of varying degree of difficulty as well as references to the literature and publicly available software make the text suitable for a graduate course.

Readership

Graduate students and research mathematicians interested in geometry and topology.

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.