01968nam a2200349 i 4500991000330819707536090714s2008 sz a b 001 0 eng d97830371905243037190523b13842109-39ule_instDip.to Matematicaeng511.33AMS 52C07AMS 52B20AMS 05A15LC QA171.5.B38Barvinok, Alexander322075Integer points in polyhedra /Alexander BarvinokZurich :European Mathematical Society,2008viii, 189 p. :ill. ;24 cmZurich lectures in advanced mathematicsIncludes bibliographical references (p. [187]-189) and indexThe algebra of polyhedra ; Linear transformations and polyhedra ; The structure of polyhedra ; Polarity ; Tangent cones : decompositions modulo polyhedra with lines ; Open polyhedra ; The exponential valuation ; Computing volumes ; Lattices, bases, and parallelepipeds ; The Minkowski convex body theorem ; Reduced basis ; Exponential sums and generating functions ; Totally unimodular polytopes ; Decomposing a 2-dimensional cone into unimodular cones via continued fractions ; Decomposing a rational cone of an arbitrary dimension into unimodular cones ; Efficient counting of integer points in rational polytopes ; The polynomial behavior of the number of integer points in polytopes ; A valuation on rational cones ; A "local" formula for the number of integer points in a polytopePolyhedral functionsLattice theoryPolynomials.b1384210928-01-1414-07-09991000330819707536LE013 52C BAR11 (2008)12013000292120le013pE35.58-l- 06060.i1499514130-07-09Integer points in polyhedra229594UNISALENTOle01314-07-09ma -engsz 00