Walk through Combinatorics, A: an Introduction to Enumeration and Graph Theory

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Walk through Combinatorics, A: an Introduction to Enumeration and Graph Theory

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  • 製本 Hardcover:ハードカバー版／ページ数 424 p.
  • 言語 ENG
  • 商品コード 9789810249007
  • DDC分類 511.6

Full Description

This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of exercises, ranging in difficulty from "routine" to "worthy of independent publication", is included. In each section, there are also exercises that contain material not explicitly discussed in the text before, so as to provide instructors with extra choices if they want to shift the emphasis of their course.It goes without saying that the text covers the classic areas, i.e. combinatorial choice problems and graph theory. What is unusual, for an undergraduate textbook, is that the author has included a number of more elaborate concepts, such as Ramsey theory, the probabilistic method and — probably the first of its kind — pattern avoidance. While the reader can only skim the surface of these areas, the author believes that they are interesting enough to catch the attention of some students. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.

Contents

Enumerative Combinatorics: The Pigeon-Hole Principle; The Principle of Mathematical induction; Basic Enumeration (Permutations and Lists of Sets and Multisets); Enumeration of Subsets, and the Binomial Theorem; Partitions, Ferrers Shapes, and Stirling Numbers; Generating Functions; Permutations and Their Subsequences; Graph Theory: The Notion of Graphs. Eulerian Circles; Trees and Forests; Planar Graphs; Coloring Problems; Graphs and Matrices; Matching Theory and Matroids; Horizons: Ramsey Theory; The Probabilistic Method; Partially Ordered Sets; Lattices.