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See below for a selection of the latest books from Combinatorics & graph theory category. Presented with a red border are the Combinatorics & graph theory books that have been lovingly read and reviewed by the experts at Lovereading. With expert reading recommendations made by people with a passion for books and some unique features Lovereading will help you find great Combinatorics & graph theory books and those from many more genres to read that will keep you inspired and entertained. And it's all free!
Eschewing the standard dry and static writing style of traditional textbooks, Discrete Explorations provides a refreshing approach to discrete mathematics. The author combines traditional course topics with popular culture, applications, and various historical examples. This book focuses on the historical development of the subject and provides details on the people behind mathematics and their motivations, which will deepen readers' appreciation of mathematics. With its unique style, the book covers many of the same topics found in other texts but done in an alternative, entertaining style that better captures readers' attention. Defining discrete mathematics, the author also covers many different topics. These include combinatorics, fractals, permutations, difference equations, graph theory, trees and financial mathematics. Not only will readers gain a greater impression of mathematics, but they'll be encouraged to further explore the subject. Highlights: Features fascinating historical references to motivate readers Text includes numerous pop culture references throughout to provide a more engaging reading experience Its unique topic structure presents a fresh approach The text's narrative style reads more like a popular book instead of a dry textbook Covers many topics from combinatorics, as well as discrete mathematics
This volume collects together research and survey papers written by invited speakers of the conference celebrating the 70th birthday of Laszlo Lovasz. The topics covered include classical subjects such as extremal graph theory, coding theory, design theory, applications of linear algebra and combinatorial optimization, as well as recent trends such as extensions of graph limits, online or statistical versions of classical combinatorial problems, and new methods of derandomization. Laszlo Lovasz is one of the pioneers in the interplay between discrete and continuous mathematics, and is a master at establishing unexpected connections, building bridges between seemingly distant fields. His invariably elegant and powerful ideas have produced new subfields in many areas, and his outstanding scientific work has defined and shaped many research directions in the last 50 years. The 14 contributions presented in this volume, all of which are connected to Laszlo Lovasz's areas of research, offer an excellent overview of the state of the art of combinatorics and related topics and will be of interest to experienced specialists as well as young researchers.
The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement. The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement. Joyal's theory of combinatorial species, ideas from Tits' theory of buildings, and Rota's work on incidence algebras inspire and find a common expression in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuffle, and establish the Borel-Hopf, Poincare-Birkhoff-Witt,and Cartier-Milnor-Moore theorems in this setting. This monograph opens a vast new area of research. It will be of interest to students and researchers working in the areas of hyperplane arrangements, semigroup theory, Hopf algebras, algebraic Lie theory, operads, and category theory.
Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.
This book discusses cryptographic and combinatorial properties of Boolean functions. Boolean functions are very easy to understand (but deep in analysis) and the subject covers significant amount of material in digital circuits, communication theory, VLSI design, computer science, coding theory and Mathematics. Boolean function is considered as one of the most basic building blocks in cryptographic system design. The properties that make a Boolean function suitable for a cryptographic system, are mostly combinatorial. We discuss these properties (e.g., balancedness, nonlinearity, correlation immunity, propagation characteristics, algebraic immunity) in detail. For each of the properties, existing research results and the recent contributions in the literature will be presented. The basic material will always contain hardcore theoretical results. However, we present the materials in a way that a person with undergraduate level mathematical background can access it. Implementation details related to these properties (e.g., how to check in writing a program whether a Boolean function is correlation immune) will be detailed.In addition to theoretical construction techniques for Boolean functions with different combinatorial and cryptographic properties, the book will concentrate on different state-of-the-art search techniques. In some cases these search techniques provide better results than the construction techniques for low number of input variables and they are quite interesting as the size of the complete set of Boolean functions is super exponential in the number of input variables. Different symmetries in the set of Boolean functions will also be presented in detail. The author will present the inherent beauty of Boolean functions that he has experienced in his research career.
The concept of a graph is fundamental in mathematics since it conveniently encodes diverse relations and facilitates combinatorial analysis of many complicated counting problems. In this book, the authors have traced the origins of graph theory from its humble beginnings of recreational mathematics to its modern setting for modeling communication networks as is evidenced by the World Wide Web graph used by many Internet search engines. This book is an introduction to graph theory and combinatorial analysis. It is based on courses given by the second author at Queen's University at Kingston, Ontario, Canada between 2002 and 2008. The courses were aimed at students in their final year of their undergraduate program.
This text grew out of an advanced course taught by the author at the Fourier Institute (Grenoble, France). It serves as an introduction to the combinatorics of symmetric functions, more precisely to Schur and Schubert polynomials. Also studied is the geometry of Grassmannians, flag varieties, and especially, their Schubert varieties. This book examines profound connections that unite these two subjects. The book is divided into three chapters. The first is devoted to symmetric functions and especially to Schur polynomials. These are polynomials with positive integer coefficients in which each of the monomials correspond to a Young tableau with the property of being 'semistandard'. The second chapter is devoted to Schubert polynomials, which were discovered by A. Lascoux and M. P. Schutzenberger who deeply probed their combinatorial properties.It is shown, for example, that these polynomials support the subtle connections between problems of enumeration of reduced decompositions of permutations and the Littlewood-Richardson rule, a particularly efficacious version of which may be derived from these connections. The final chapter is geometric. It is devoted to Schubert varieties, subvarieties of Grassmannians, and flag varieties defined by certain incidence conditions with fixed subspaces. This volume makes accessible a number of results, creating a solid stepping stone for scaling more ambitious heights in the area. The author's intent was to remain elementary: The first two chapters require no prior knowledge, the third chapter uses some rudimentary notions of topology and algebraic geometry. For this reason, a comprehensive appendix on the topology of algebraic varieties is provided. This book is the English translation of a text previously published in French.
The infinite-dimensional groups in the title refer to unitary groups of Hilbert spaces, the infinite symmetric group, groups of homeomorphisms of manifolds, groups of transformations of measure spaces, etc. The book presents an approach to the study of such groups based on ideas from geometric functional analysis and from exploring the interplay between dynamical properties of those groups, combinatorial Ramsey-type theorems, and the phenomenon of concentration of measure. The dynamics of infinite-dimensional groups is very much unlike that of locally compact groups. For instance, every locally compact group acts freely on a suitable compact space (Veech). By contrast, a 1983 result by Gromov and Milman states that whenever the unitary group of a separable Hilbert space continuously acts on a compact space, it has a common fixed point. In the book, this new fast-growing theory is built strictly from well-understood examples up. The book has no close counterpart and is based on recent research articles. At the same time, it is organized so as to be reasonably self-contained. The topic is essentially interdisciplinary and will be of interest to mathematicians working in geometric functional analysis, topological and ergodic dynamics, Ramsey theory, logic and descriptive set theory, representation theory, topological groups, and operator algebras.
In the world of mathematics and computer science, technological advancements are constantly being researched and applied to ongoing issues. Setbacks in social networking, engineering, and automation are themes that affect everyday life, and researchers have been looking for new techniques in which to solve these challenges. Graph theory is a widely studied topic that is now being applied to real-life problems. Advanced Applications of Graph Theory in Modern Society is an essential reference source that discusses recent developments on graph theory, as well as its representation in social networks, artificial neural networks, and many complex networks. The book aims to study results that are useful in the fields of robotics and machine learning and will examine different engineering issues that are closely related to fuzzy graph theory. Featuring research on topics such as artificial neural systems and robotics, this book is ideally designed for mathematicians, research scholars, practitioners, professionals, engineers, and students seeking an innovative overview of graphic theory.
Graph algebras are a family of operator algebras which are associated to directed graphs. These algebras have an attractive structure theory in which algebraic properties of the algebra are related to the behavior of paths in the underlying graph. In the past few years there has been a great deal of activity in this area, and graph algebras have cropped up in a surprising variety of situations, including non-abelian duality, non-commutative geometry, and the classification of simple $C^*$-algebras.The first part of the book provides an introduction to the subject suitable for students who have seen a first course on the basics of $C^*$-algebras. In the second part, the author surveys the literature on the structure theory of graph algebras, highlights some applications of this theory, and discusses several recent generalizations which seem particularly promising. The volume is suitable for graduate students and research mathematicians interested in graph theory and operator algebras.
This book presents rigidity theory in a historical context. The combinatorial aspects of rigidity are isolated and framed in terms of a special class of matroids, which are a natural generalization of the connectivity matroid of a graph. This book includes an introduction to matroid theory and an extensive study of planar rigidity. The final chapter is devoted to higher-dimensional rigidity, highlighting the main open questions. Also included is an extensive annotated bibliography with over 150 entries. This book is aimed at graduate students and researchers in graph theory and combinatorics or in fields which apply the structural aspects of these subjects in architecture and engineering. Accessible to those who have had an introduction to graph theory at the senior or graduate level, this book is suitable for a graduate course in graph theory.
This book contains detailed descriptions of the many exciting recent developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials, which are described in Appendix A. The book is appropriate as a text for a topics course in algebraic combinatorics, a volume for self-study, or a reference text for researchers in any area which involves symmetric functions or lattice path combinatorics.