Foundations of Combinatorics with Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Combinatorics with Applications write by Edward A. Bender. This book was released on 2013-01-18. Foundations of Combinatorics with Applications available in PDF, EPUB and Kindle. This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.
Foundations of Applied Combinatorics
Foundations of Applied Combinatorics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Applied Combinatorics write by Edward A. Bender. This book was released on 1991. Foundations of Applied Combinatorics available in PDF, EPUB and Kindle. This introduction to combinatorics is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises (some with solutions), notes, and references appear throughout the text. 75 figures. Appendixes.
Foundations of Combinatorial Topology
Foundations of Combinatorial Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Combinatorial Topology write by L. S. Pontryagin. This book was released on 2015-05-20. Foundations of Combinatorial Topology available in PDF, EPUB and Kindle. Concise, rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Lucid coverage of the field includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete and careful manner. A beneficial text for a graduate-level course, "this little book is an extremely valuable addition to the literature of algebraic topology." — The Mathematical Gazette.
Analytic Combinatorics
Analytic Combinatorics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analytic Combinatorics write by Philippe Flajolet. This book was released on 2009-01-15. Analytic Combinatorics available in PDF, EPUB and Kindle. 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.
Matrices in Combinatorics and Graph Theory
Matrices in Combinatorics and Graph Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Matrices in Combinatorics and Graph Theory write by Bolian Liu. This book was released on 2013-03-09. Matrices in Combinatorics and Graph Theory available in PDF, EPUB and Kindle. Combinatorics and Matrix Theory have a symbiotic, or mutually beneficial, relationship. This relationship is discussed in my paper The symbiotic relationship of combinatorics and matrix theoryl where I attempted to justify this description. One could say that a more detailed justification was given in my book with H. J. Ryser entitled Combinatorial Matrix Theon? where an attempt was made to give a broad picture of the use of combinatorial ideas in matrix theory and the use of matrix theory in proving theorems which, at least on the surface, are combinatorial in nature. In the book by Liu and Lai, this picture is enlarged and expanded to include recent developments and contributions of Chinese mathematicians, many of which have not been readily available to those of us who are unfamiliar with Chinese journals. Necessarily, there is some overlap with the book Combinatorial Matrix Theory. Some of the additional topics include: spectra of graphs, eulerian graph problems, Shannon capacity, generalized inverses of Boolean matrices, matrix rearrangements, and matrix completions. A topic to which many Chinese mathematicians have made substantial contributions is the combinatorial analysis of powers of nonnegative matrices, and a large chapter is devoted to this topic. This book should be a valuable resource for mathematicians working in the area of combinatorial matrix theory. Richard A. Brualdi University of Wisconsin - Madison 1 Linear Alg. Applies., vols. 162-4, 1992, 65-105 2Camhridge University Press, 1991.
