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Probabilistic Methods in Combinatorial Analysis
This work explores the role of probabilistic methods for solving combinatorial problems. The subjects studied are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these define the probabilistic setting of Sachkov's general combinatorial scheme. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods. This important book describes many ideas not previously available in English and will be of interest to graduate students and professionals in mathematics and probability theory.
Combinatory Analysis, Volumes I and II
By “combinatory analysis”, the author understands the part of combinatorics now known as “algebraic combinatorics”. In this book, the classical results of the outstanding 19th century school of British mathematicians are presented with great clarity and completeness. From the Introduction (1915): “The object of this work is, in the main, to present to mathematicians an account of theorems in combinatory analysis which are of a perfectly general character, and to show the connection between them by as far as possible bringing them together as parts of a general doctrine. It may appeal also to others whose reading has not been very extensive. They may not improbably find here some new points of view and suggestions which may prompt them to original investigation in a fascinating subject … “In the present volume there appears a certain amount of original matter which has not before been published. It involves the author's preliminary researches in combinatory theory which have been carried out during the last thirty years. For the most part it is original work which, however, owes much to valuable papers by Cayley, Sylvester, and Hammond.”
The Rise and Fall of the German Combinatorial Analysis
This text presents the ideas of a particular group of mathematicians of the late 18th century known as “the German combinatorial school” and its influence. The book tackles several questions concerning the emergence and historical development of the German combinatorial analysis, which was the unfinished scientific research project of that group of mathematicians. The historical survey covers the three main episodes in the evolution of that research project: its theoretical antecedents (which go back to the innovative ideas on mathematical analysis of the late 17th century) and first formulation, its consolidation as a foundationalist project of mathematical analysis, and its dissolution at the beginning of the 19th century. In addition, the book analyzes the influence of the ideas of the combinatorial school on German mathematics throughout the 19th century.
Combinatory Analysis
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Analytic Combinatorics
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Probabilistic Methods in Combinatorial Analysis
This work explores the role of probabilistic methods for solving combinatorial problems. The subjects studied are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these define the probabilistic setting of Sachkov's general combinatorial scheme. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods. This important book describes many ideas not previously available in English and will be of interest to graduate students and professionals in mathematics and probability theory.
Combinatorial Designs
Created to teach students many of the most important techniques used for constructing combinatorial designs, this is an ideal textbook for advanced undergraduate and graduate courses in combinatorial design theory. The text features clear explanations of basic designs, such as Steiner and Kirkman triple systems, mutual orthogonal Latin squares, finite projective and affine planes, and Steiner quadruple systems. In these settings, the student will master various construction techniques, both classic and modern, and will be well-prepared to construct a vast array of combinatorial designs. Design theory offers a progressive approach to the subject, with carefully ordered results. It begins with simple constructions that gradually increase in complexity. Each design has a construction that contains new ideas or that reinforces and builds upon similar ideas previously introduced. A new text/reference covering all apsects of modern combinatorial design theory. Graduates and professionals in computer science, applied mathematics, combinatorics, and applied statistics will find the book an essential resource.
