Integer Programming, Combinatorics, and Splines

Abstract

In this chapter we will consider a series of interrelated topics concerning polyhedral regions P in ℝⁿ, the integer points in these regions, and piece-wise polynomial functions on subdivisions of such regions. In each case Gröbner basis techniques give important computational and conceptual tools to deal with problems of interest and practical importance. These topics are also closely related to the material on polytopes and toric varieties from Chapter 7, but we have tried to make this chapter as independent as possible from Chapter 7 so that it can be read separately.