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Discrete geometry and symmetrydedica...

Conder, Marston D. E.

Discrete geometry and symmetrydedicated to Karoly Bezdek and Egon Schulte on the occasion of their 60th birthdays /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Discrete geometry and symmetryedited by Marston D. E. Conder, Antoine Deza, Asia Ivic Weiss.
Reminder of title:	dedicated to Karoly Bezdek and Egon Schulte on the occasion of their 60th birthdays /
other author:	Conder, Marston D. E.
Published:	Cham :Springer International Publishing :2018.
Description:	xxiii, 333 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Mathematics.
Online resource:	http://dx.doi.org/10.1007/978-3-319-78434-2
ISBN:	9783319784342$q(electronic bk.)

Discrete geometry and symmetrydedicated to Karoly Bezdek and Egon Schulte on the occasion of their 60th birthdays /
Discrete geometry and symmetrydedicated to Karoly Bezdek and Egon Schulte on the occasion of their 60th birthdays /[electronic resource] :edited by Marston D. E. Conder, Antoine Deza, Asia Ivic Weiss. - Cham :Springer International Publishing :2018. - xxiii, 333 p. :ill. (some col.), digital ;24 cm. - Springer proceedings in mathematics & statistics,v.2342194-1009 ;. - Springer proceedings in mathematics & statistics ;v.19..

The geometry of homothetic covering and illumination -- Stability of the simplex bound for packings by equal spherical caps determined by simplicial regular polytopes -- Vertex-transitive Haar graphs that are not Cayley graphs -- On the Volume of Boolean Expressions of Large Congruent Balls -- Small Primitive Zonotopes -- Delone Sets: Local Identity and Global Symmetry -- The Twist Operator on Maniplexes -- Hexagonal Extensions of Toroidal Maps and Hypermaps -- Noncongruent Equidissections of the Plane -- Pascal's triangle of configurations -- Volume of Convex Hull of Two Bodies and Related Problems -- Integers, Modular Groups, and Hyperbolic Space -- Monge points, Euler lines, and Feuerbach spheres in Minkowski spaces -- An Algorithm for Classification of Fundamental Polygons for a Plane Discontinuous Group -- Self-inscribed regular hyperbolic honeycombs -- Sphere-of-Influence graphs in Normed Spaces -- On Symmetries of Projections and Sections of Convex Bodies -- Regular Incidence Complexes, Polytopes, and C-Groups.

This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference "Geometry and Symmetry" in Veszprem, Hungary from 29 June to 3 July 2015. The conference was dedicated to Karoly Bezdek and Egon Schulte on the occasion of their 60th birthdays, acknowledging their highly regarded contributions in these fields. While the classical problems of discrete geometry have a strong connection to geometric analysis, coding theory, symmetry groups, and number theory, their connection to combinatorics and optimization has become of particular importance. The last decades have seen a revival of interest in discrete geometric structures and their symmetry. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory and geometry, combinatorial group theory, and hyperbolic geometry and topology. This book contains papers on new developments in these areas, including convex and abstract polytopes and their recent generalizations, tiling and packing, zonotopes, isoperimetric inequalities, and on the geometric and combinatorial aspects of linear optimization. The book is a valuable resource for researchers, both junior and senior, in the field of discrete geometry, combinatorics, or discrete optimization. Graduate students find state-of-the-art surveys and an open problem collection.

ISBN: 9783319784342$q(electronic bk.)

Standard No.: 10.1007/978-3-319-78434-2doiSubjects--Topical Terms:

184409
Mathematics.

LC Class. No.: QA640.7 / .D573 2018

Dewey Class. No.: 516.13

Discrete geometry and symmetrydedicated to Karoly Bezdek and Egon Schulte on the occasion of their 60th birthdays /
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505 0 $a The geometry of homothetic covering and illumination -- Stability of the simplex bound for packings by equal spherical caps determined by simplicial regular polytopes -- Vertex-transitive Haar graphs that are not Cayley graphs -- On the Volume of Boolean Expressions of Large Congruent Balls -- Small Primitive Zonotopes -- Delone Sets: Local Identity and Global Symmetry -- The Twist Operator on Maniplexes -- Hexagonal Extensions of Toroidal Maps and Hypermaps -- Noncongruent Equidissections of the Plane -- Pascal's triangle of configurations -- Volume of Convex Hull of Two Bodies and Related Problems -- Integers, Modular Groups, and Hyperbolic Space -- Monge points, Euler lines, and Feuerbach spheres in Minkowski spaces -- An Algorithm for Classification of Fundamental Polygons for a Plane Discontinuous Group -- Self-inscribed regular hyperbolic honeycombs -- Sphere-of-Influence graphs in Normed Spaces -- On Symmetries of Projections and Sections of Convex Bodies -- Regular Incidence Complexes, Polytopes, and C-Groups.
520 $a This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference "Geometry and Symmetry" in Veszprem, Hungary from 29 June to 3 July 2015. The conference was dedicated to Karoly Bezdek and Egon Schulte on the occasion of their 60th birthdays, acknowledging their highly regarded contributions in these fields. While the classical problems of discrete geometry have a strong connection to geometric analysis, coding theory, symmetry groups, and number theory, their connection to combinatorics and optimization has become of particular importance. The last decades have seen a revival of interest in discrete geometric structures and their symmetry. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory and geometry, combinatorial group theory, and hyperbolic geometry and topology. This book contains papers on new developments in these areas, including convex and abstract polytopes and their recent generalizations, tiling and packing, zonotopes, isoperimetric inequalities, and on the geometric and combinatorial aspects of linear optimization. The book is a valuable resource for researchers, both junior and senior, in the field of discrete geometry, combinatorics, or discrete optimization. Graduate students find state-of-the-art surveys and an open problem collection.
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