Das Gebiet des Zahlens von Gitterpunkten in Polytopen," auch Ehrhart-Theorie genannt, bietet verschiedene Verbindungen zu elementarer endlicher Fourier-Analysis, Erzeugendenfunktionen, dem Munzenproblem von Frobenius, Raumwinkeln, magischen Quadraten, Dedekind-Summen, algorithmischer Geometrie und mehr. Die Autoren haben mit dem Buch einen roten Faden geknupft, der diese Verbindungen aufzeigt und so die grundlegenden und dennoch tiefgehenden Ideen aus diskreter Geometrie, Kombinatorik und Zahlentheorie anschaulich verbindet.
Mit 250 Aufgaben und offenen Problemen fuhlt sich der...
Das Gebiet des Zahlens von Gitterpunkten in Polytopen," auch Ehrhart-Theorie genannt, bietet verschiedene Verbindungen zu elementarer endlicher Fou...
The world is continuous, but the mind is discrete. David Mumford We seek to bridge some critical gaps between various ?elds of mathematics by studying the interplay between the continuous volume and the discrete v- ume of polytopes. Examples of polytopes in three dimensions include crystals, boxes, tetrahedra, and any convex object whose faces are all ?at. It is amusing to see how many problems in combinatorics, number theory, and many other mathematical areas can be recast in the language of polytopes that exist in some Euclidean space. Conversely, the versatile structure of polytopes gives...
The world is continuous, but the mind is discrete. David Mumford We seek to bridge some critical gaps between various ?elds of mathematics by studying...
This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. Because there is no other book that puts together all of these ideas in one place, this text is truly a service to the mathematical community.
We encounter here a friendly invitation to the field of "counting integer points in polytopes," also known as Ehrhart theory, and its various connections to elementary finite...
This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The autho...
