Existence of Unimodular Triangulations–Positive Results

Know about the book -

Existence of Unimodular Triangulations–Positive Results is written by Christian Haase and published by American Mathematical Soc.. It's available with International Standard Book Number or ISBN identification 1470447169 (ISBN 10) and 9781470447168 (ISBN 13).

Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor.