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

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Release : 2019-05-30
Genre : Mathematics
Kind : eBook
Book Rating : 491/5 ( reviews)

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Book Synopsis Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes by : Hibi Takayuki

Download or read book Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes written by Hibi Takayuki. This book was released on 2019-05-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic and Geometric Combinatorics on Lattice Polytopes

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Author :
Release : 2019
Genre : Polytopes
Kind : eBook
Book Rating : 472/5 ( reviews)

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Book Synopsis Algebraic and Geometric Combinatorics on Lattice Polytopes by : Takayuki Hibi

Download or read book Algebraic and Geometric Combinatorics on Lattice Polytopes written by Takayuki Hibi. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of research papers and expository survey articles presented by the invited speakers of the workshop 'Algebraic and Geometric Combinatorics 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 development of many research areas surrounding lattice polytopes. With the survey articles, research papers and open problems, graduate students can learn fundamental materials on lattice polytopes and researchers can find exciting activities and avenues for further exploration on lattice polytopes.

Algebraic and Geometric Combinatorics

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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 800/5 ( reviews)

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Book Synopsis Algebraic and Geometric Combinatorics by : Christos A. Athanasiadis

Download or read book Algebraic and Geometric Combinatorics written by Christos A. Athanasiadis. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains original research and survey articles stemming from the Euroconference ``Algebraic and Geometric Combinatorics''. The papers discuss a wide range of problems that illustrate interactions of combinatorics with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and partially ordered sets. Among the topics covered are combinatorics of polytopes, lattice polytopes, triangulations and subdivisions, Cohen-Macaulay cell complexes, monomial ideals, geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig combinatorics, and graph colorings. This book is aimed at researchers and graduate students interested in various aspects of modern combinatorial theories.

Lectures in Geometric Combinatorics

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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 402/5 ( reviews)

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Book Synopsis Lectures in Geometric Combinatorics by : Rekha R. Thomas

Download or read book Lectures in Geometric Combinatorics written by Rekha R. Thomas. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the statepolytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Grobner bases of toric ideals and other methods fromcommutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.

Interactions with Lattice Polytopes

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Release : 2022-06-08
Genre : Mathematics
Kind : eBook
Book Rating : 277/5 ( reviews)

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Book Synopsis Interactions with Lattice Polytopes by : Alexander M. Kasprzyk

Download or read book Interactions with Lattice Polytopes written by Alexander M. Kasprzyk. This book was released on 2022-06-08. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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