Lattice Points In Simple Polytopes

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Lattice Points In Simple Polytopes

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Author : M. Brion
language : en
Publisher:
Release Date : 1995

Lattice Points In Simple Polytopes written by M. Brion and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.

Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes

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Author : Hibi Takayuki
language : en
Publisher: World Scientific
Release Date : 2019-05-30

Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes written by Hibi Takayuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-30 with Mathematics categories.

This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.

Lattice Points

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Author : Paul Erdős
language : en
Publisher: Longman Scientific and Technical
Release Date : 1989

Lattice Points written by Paul Erdős and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

Contains solved and unsolved problems concerning lattice points, especially geometric, number theoretic, combinatorial, and analytic results, theories, and problems related to lattice points. Emphasis is on the geometry of numbers. Provides extensive comments on each problem, consisting mostly of heuristic arguments and intuitive descriptions. There are only a few proofs. Annotation copyrighted by Book News, Inc., Portland, OR

Lattice Points Inside Lattice Polytopes

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Author : Oleg Pikhurko
language : en
Publisher:
Release Date : 2000

Lattice Points Inside Lattice Polytopes written by Oleg Pikhurko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.

Interactions With Lattice Polytopes

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Author : Alexander M. Kasprzyk
language : en
Publisher: Springer Nature
Release Date : 2022-06-08

Interactions With Lattice Polytopes written by Alexander M. Kasprzyk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-08 with Mathematics categories.

This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes in modern mathematics. Covering a diverse range of topics, including algebraic geometry, mirror symmetry, symplectic geometry, discrete geometry, and algebraic combinatorics, the common theme is the study of lattice polytopes. These fascinating combinatorial objects are a cornerstone of toric geometry and continue to find rich and unforeseen applications throughout mathematics. The workshop Interactions with Lattice Polytopes assembled many top researchers at the Otto-von-Guericke-Universität Magdeburg in 2017 to discuss the role of lattice polytopes in their work, and many of their presented results are collected in this book. Intended to be accessible, these articles are suitable for researchers and graduate students interested in learning about some of the wide-ranging interactions of lattice polytopes in pure mathematics.

Positive Polynomials Convex Integral Polytopes And A Random Walk Problem

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Author : David E. Handelman
language : en
Publisher: Springer
Release Date : 2006-11-15

Positive Polynomials Convex Integral Polytopes And A Random Walk Problem written by David E. Handelman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Emanating from the theory of C*-algebras and actions of tori theoren, the problems discussed here are outgrowths of random walk problems on lattices. An AGL (d,Z)-invariant (which is a partially ordered commutative algebra) is obtained for lattice polytopes (compact convex polytopes in Euclidean space whose vertices lie in Zd), and certain algebraic properties of the algebra are related to geometric properties of the polytope. There are also strong connections with convex analysis, Choquet theory, and reflection groups. This book serves as both an introduction to and a research monograph on the many interconnections between these topics, that arise out of questions of the following type: Let f be a (Laurent) polynomial in several real variables, and let P be a (Laurent) polynomial with only positive coefficients; decide under what circumstances there exists an integer n such that Pnf itself also has only positive coefficients. It is intended to reach and be of interest to a general mathematical audience as well as specialists in the areas mentioned.

Notes On Lattice Points Of Zonotopes And Lattice Face Polytopes

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Author :
language : en
Publisher:
Release Date : 2010

Notes On Lattice Points Of Zonotopes And Lattice Face Polytopes written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.

Computing The Continuous Discretely

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Author : Matthias Beck
language : en
Publisher: Springer
Release Date : 2015-11-14

Computing The Continuous Discretely written by Matthias Beck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-14 with Mathematics categories.

This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE

The Number Of Lattice Points In Irrational Polytopes

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Author : Bence Borda
language : en
Publisher:
Release Date : 2016

The Number Of Lattice Points In Irrational Polytopes written by Bence Borda and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Lattice theory categories.

Lattice Point Counting With Applications To Integer Programming

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Author : Timothy J. Folts
language : en
Publisher:
Release Date : 2009

Lattice Point Counting With Applications To Integer Programming written by Timothy J. Folts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Integer programming categories.

Counting lattice points in a polytope is a classical problem in computer science and combinatorics. As the polytope scales to larger sizes the number of lattice points increases. Finding the optimal solution or solutions to an integer programming problem is much harder than in a linear program as the optimal solution or solutions do not necessarily lie on a boundary of the space being considered. Using functions whose power series expansions can be used to represent the integer points in a space allows for several useful properties to arise. A theorem by Michel Brion states that when using such representations the integer points within a convex polytope can be represented as the summation of the representations of the integer points in the infinite cones defined by each vertex of the polytope. By finding short vectors of a lattice and using them to define the lattice within a polytope, coupled with repeatedly testing different level curves of the given linear function, we may solve any integer program.