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This book provides the solutions to all 347 exercises contained in the text Convexity from the Geometric Point of View, published in the same Cornerstones series. All these exercises are restated and numbered analogously to those in the original text. The corresponding...
Algorithmic Aspects of Combinatorics
An Introduction to Discrete Mathematics offers an engaging and accessible introduction to discrete mathematics for beginning undergraduate students across a wide range of application areas, from mathematics to statistics, operations research, business, engineering, and...
Oriented matroids appear throughout discrete geometry, with applications in algebra, topology, physics, and data analysis. This introduction to oriented matroids is intended for graduate students, scientists wanting to apply oriented matroids, and researchers in pure...
Abstract polytopes are partially ordered sets that satisfy some key aspects of the face lattices of convex polytopes. They are chiral if they have maximal symmetry by combinatorial rotations, but none by combinatorial reflections. Aimed at graduate students and...
In diesem Buch werden die bekannten Methoden zur Konstruktion magischer Quadrate mit weiteren (über die notwendigen Eigenschaften magischer Quadrate hinausgehenden) speziellen Eigenschaften verständlich und detailliert vorgestellt: Konstruiert werden etwa...
Die faszinierende Geschichte der magischen Quadrate ist reich an sehr unterschiedlichen Konstruktionsverfahren, die von der Antike bis in die Neuzeit reichen und die hier erstmals alle in einem Buch präsentiert werden: Dieses Werk bietet einen umfassenden und...
This book features carefully selected research papers presented during the 9th International Conference on Discrete Mathematics and Mathematical Modelling in the Digital Era (ICDMMMDE-2023). The conference, organised at the Department of Mathematics, The Gandhigram...
Recent advances in AI and Mechanism Design provide a vital tool for solving collective action problems, common in international relations. By using AI to optimize mechanisms for cooperation and coordination, we can better address issues such as climate change, trade,...
Fractional Calculus: Bridging Theory with Computational and Contemporary Advances is an authoritative and comprehensive guide that delves into the world of fractional calculus, offering a unique blend of theoretical foundations, numerical algorithms, practical...
This volume contains nine survey articles by the invited speakers of the 30th British Combinatorial Conference, held at Queen Mary University of London in July 2024. Each article provides an overview of recent developments in a current hot research topic in...
The International Conference on Complex Networks (CompleNet) brings together researchers and practitioners from diverse disciplines working on areas related to complex networks. CompleNet has been an active conference since 2009. Over the past two decades, we have...
Beginning with its origins in the pioneering work of W.T. Tutte in 1947, this monograph systematically traces through some of the impressive developments in matching theory. A graph is matchable if it has a perfect matching. A matching covered graph is a connected...
This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not...
Brooks' Theorem (1941) is one of the most famous and fundamental theorems in graph theory – it is mentioned/treated in all general monographs on graph theory. It has sparked research in several directions. This book presents a comprehensive overview of this development...
Critical coding techniques have developed over the past few decades for data storage, retrieval and transmission systems, significantly mitigating costs for governments and corporations that maintain server systems containing large amounts of data. This book surveys the...
The focus of this monograph is converting—reshaping—one 3D convex polyhedron to another via an operation the authors call “tailoring.” A convex polyhedron is a gem-like shape composed of flat facets, the focus of study since Plato and Euclid.The tailoring operation...
Discrete structures model a vast array of objects ranging from DNA sequences to internet networks. The theory of generating functions provides an algebraic framework for discrete structures to be enumerated using mathematical tools. This book is the result of 25 years...
This book focuses on the theoretical side of temporal network research and gives an overview of the state of the art in the field. Curated by two pioneers in the field who have helped to shape it, the book contains contributions from many leading researchers....
This book discusses discrete geometric analysis, especially topological crystallography and discrete surface theory for trivalent discrete surfaces. Topological crystallography, based on graph theory, provides the most symmetric structure among given combinatorial...
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