English

Foundation of Combinatorics with Applications

Parts I and II deal with two fundamental aspects of combinatorics: enumeration and graph theory. �Enumeration� can mean either counting or listing things. Mathematicians have generally limited their attention to counting, but listing plays an important role in computer science, so we discuss both aspects. After introducing the basic concepts of �graph theory� in Part II, we present a variety of applications of interest in computer science and mathematics. Induction and recursion play a fundamental role in mathematics. The usefulness of recursion in computer science and in its interaction with combinatorics is the subject of Part III. In Part IV we look at �generating functions,� a powerful tool for studying counting problems.

Sign in with your free account to read, download EPUBs or listen.