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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.
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.
This book contains recent contributions to the fields of rigidity
and symmetry with two primary focuses: to present the
mathematically rigorous treatment of rigidity of structures and to
explore the interaction of geometry, algebra and combinatorics.
Contributions present recent trends and advances in discrete
geometry, particularly in the theory of polytopes. 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, classical geometry, hyperbolic
geometry and topology. Overall, the book shows how researchers from
diverse backgrounds explore connections among the various discrete
structures with symmetry as the unifying theme. The volume will be
a valuable source as an introduction to the ideas of both
combinatorial and geometric rigidity theory and its applications,
incorporating the surprising impact of symmetry. It will appeal to
students at both the advanced undergraduate and graduate levels, as
well as post docs, structural engineers and chemists.
This book contains recent contributions to the fields of rigidity
and symmetry with two primary focuses: to present the
mathematically rigorous treatment of rigidity of structures and to
explore the interaction of geometry, algebra and combinatorics.
Contributions present recent trends and advances in discrete
geometry, particularly in the theory of polytopes. 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, classical geometry, hyperbolic
geometry and topology. Overall, the book shows how researchers from
diverse backgrounds explore connections among the various discrete
structures with symmetry as the unifying theme. The volume will be
a valuable source as an introduction to the ideas of both
combinatorial and geometric rigidity theory and its applications,
incorporating the surprising impact of symmetry. It will appeal to
students at both the advanced undergraduate and graduate levels, as
well as post docs, structural engineers and chemists.
The aim of this volume is to reinforce the interaction between the
three main branches (abstract, convex and computational) of the
theory of polytopes. The articles include contributions from many
of the leading experts in the field, and their topics of concern
are expositions of recent results and in-depth analyses of the
development (past and future) of the subject. The subject matter of
the book ranges from algorithms for assignment and transportation
problems to the introduction of a geometric theory of polyhedra
which need not be convex. With polytopes as the main topic of
interest, there are articles on realizations, classifications,
Eulerian posets, polyhedral subdivisions, generalized stress, the
Brunn--Minkowski theory, asymptotic approximations and the
computation of volumes and mixed volumes. For researchers in
applied and computational convexity, convex geometry and discrete
geometry at the graduate and postgraduate levels.
The aim of this volume is to reinforce the interaction between the
three main branches (abstract, convex and computational) of the
theory of polytopes. The articles include contributions from many
of the leading experts in the field, and their topics of concern
are expositions of recent results and in-depth analyses of the
development (past and future) of the subject. The subject matter of
the book ranges from algorithms for assignment and transportation
problems to the introduction of a geometric theory of polyhedra
which need not be convex. With polytopes as the main topic of
interest, there are articles on realizations, classifications,
Eulerian posets, polyhedral subdivisions, generalized stress, the
Brunn--Minkowski theory, asymptotic approximations and the
computation of volumes and mixed volumes. For researchers in
applied and computational convexity, convex geometry and discrete
geometry at the graduate and postgraduate levels.
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