Open AccessBook
Computing the Continuous Discretely: Integer-point Enumeration in Polyhedra
Matthias Beck,Sinai Robins +1 more
TLDR
The Ehrhart Theory of Reciprocity as discussed by the authors has been applied to count lattice points in polytopes and the Dehn-Sommerville relations.Abstract:
Preface.- The Coin-Exchange Problem of Frobenius.- A Gallery of Discrete Volumes.- Counting Lattice Points in Polytopes: The Ehrhart Theory.- Reciprocity.- Face Numbers and the Dehn-Sommerville Relations in Ehrhartian Terms.- Magic Squares.- Finite Fourier Analysis.- Dedekind Sums.- The Decomposition of a Polytope into Its Cones.- Euler-MacLaurin Summation in Rd.- Solid Angles.- A Discrete Version of Green's Theorem Using Elliptic Functions.- Appendix A: Triangulations of Polytopes.- Appendix B: Hints for Selected Exercises.- References.- Index.- List of Symbols.-read more
Citations
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Texture Description Through Histograms of Equivalent Patterns
TL;DR: In a comprehensive survey, it is shown that diverse texture descriptors, such as co-occurrence matrices, gray-level differences and local binary patterns, can be seen all to be examples of the HEP.
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Codes for DNA Sequence Profiles
TL;DR: This work introduces the DNA storage channel and model the read process through the use of profile vectors and proposes new asymmetric coding techniques to combat the effects of synthesis and sequencing noise.
Journal ArticleDOI
The Inverse Moment Problem for Convex Polytopes
TL;DR: It is shown that the vertices of an N-vertex convex polytope in ℝd can be reconstructed from the knowledge of O(DN) axial moments, in d+1 distinct directions in general position.
Journal ArticleDOI
Wall crossings for double Hurwitz numbers
TL;DR: Cavalieri et al. as mentioned in this paper gave a unified approach to these results and strengthened them in several ways, including the extension of the results of Shadrin et al to arbitrary genus, and the understanding of the wall crossing for these functions.
References
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Book ChapterDOI
Theorie der vielfachen Kontinuität
TL;DR: In this article, a gegenseitige Abhangigkeit zweier Variabeln zur lebhaften Anschauung bringen will, so bedient man sich haufig der ebenen Kurven, and baut so auf die geometrische Anschausauung eine Reihe von Schlussen, deren letztes Ergebnis eine rein analytische Bedeutung hat.
Book
Lectures on the Geometry of Numbers
TL;DR: In this article, Minkowski's Two Theorems and Linear Inequalities are discussed, and the theory of reduction is discussed as a solution to the problem of linear inequalities.
Book
Realization Spaces of Polytopes
TL;DR: In this article, the universality theorem and the applications of university polytopes are discussed, as well as alternative construction techniques for three-dimensional polytope construction and problems.