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This volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973. Contributors from all over the world took part and the result is a very useful and up-to-date account of what is happening in the field of combinatorics. A section of problems illustrates some of the topics in need of further investigation.

Combinatorial analysis --- 519.1 --- Congresses --- 519.1 Combinatorics. Graph theory --- Combinatorics. Graph theory --- Congresses. --- Analyse combinatoire --- Congrès --- Discrete mathematics

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This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.

Combinatorial enumeration problems. --- Enumeration problems, Combinatorial --- Combinatorial analysis --- Analyse combinatoire --- Combinatorial enumeration problems --- Problèmes combinatoires d'énumération --- 519.1 --- 519.1 Combinatorics. Graph theory --- Combinatorics. Graph theory

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Algorithmic aspects of combinatorics

Discrete mathematics --- Combinatorial analysis --- Algorithms. --- Data processing. --- 519.1 --- 681.3*G21 --- 681.3*G21 Combinatorics: combinatorial algorithms; counting problems; generating functions; permutations and combinations; recurrences and difference equations --- Combinatorics: combinatorial algorithms; counting problems; generating functions; permutations and combinations; recurrences and difference equations --- 519.1 Combinatorics. Graph theory --- Combinatorics. Graph theory --- Algorism --- Algebra --- Arithmetic --- Foundations

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Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.

Graph theory --- System Analysis --- 519.1 --- Combinatorics. Graph theory --- 519.1 Combinatorics. Graph theory --- System analysis --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Extremal problems --- Network analysis --- Network science --- System analysis. --- Graph theory.

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This book is based on a set of lectures given to a mixed audience of physicists and mathematicians. The desire to be intelligible to both groups is the underlying preoccupation of the author. Physicists nowadays are particularly interested in phase transitions. The typical situation is that a system of interacting particles exhibits an abrupt change of behaviour at a certain temperature, although the local forces between the particles are thought to be smooth functions of temperature. This account discusses the theory behind a simple model of such phenomena. An important tool is the mathematical discipline known as the Theory of Graphs. There are five chapters, each subdivided into sections. The first chapter is intended as a broad introduction to the subject, and it is written in a more informal manner than the rest. Notes and references for each chapter are given at the end of the chapter.

Phase transformations (Statistical physics) --- Graph theory. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics --- Extremal problems --- 519.1 --- 519.1 Combinatorics. Graph theory --- Combinatorics. Graph theory --- Phase transformations (Statistical physics). --- Discrete mathematics