Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
Please make all selections above before adding to cart
Copy To Clipboard
Successfully Copied!
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
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.

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.