Integer Points in Polyhedra
The main goal of this book is to lead the reader towards the most recent advances in the enumeration of in¬teger points in polyhedra. The author develops the structural theory and deals with algorithmic applica¬tions. He gives a new perspective on some of the old results, such as the role of the clas¬sical construction of continued fractions or the “continuity” property of polynomials enumerating integer points in parametric polytopes seen through the prism of identities in the algebra of polyhedra. Furthermore, the text contains new results, including the remarkable Berline–Vergne local formula. The text is based on the author’s lecture notes for a graduate course and it contains numerous figures and various exercises, and thus it is suitable for study. It requires general mathematical maturity (e.g. basic linear algebra and analysis). The combination of new and classical results, theory and algorithmic applications, up-to-date results and an original approach makes the text useful for researchers and relatively easy to read for students.