Synopses & Reviews
This balanced and comprehensive treatment of topics in discrete mathematics and statistical design raises new questions and assesses potential difficulties surrounding various techniques. Covers a broad range of topics, from counting and enumeration techniques to graphs and networks, combinatorial and statistical designs, and partially ordered sets. Presents several methods of construction, many appearing for the first time in book form. Theory is carefully developed and presented in a conversational way that gears readers toward important new ideas and illustrates the necessity of introducing new techniques. Also examines the practical applications of results. Two entire sections are devoted to Polya's and DeBruign's enumeration of results, presenting them in the form of step-by-step recipes, ready for use by research workers.
Table of Contents
Partial table of contents:
Ways to Choose.
The Essentials of Counting.
Occupancy.
More on Counting.
Exercises.
Historical Notes.
References.
Generating Functions.
The Formal Power Series.
The Combinatorial Meaning of Convolution.
Exercises.
Generating Functions for Stirling Numbers.
Bell Polynomials.
Recurrence Relations.
Exercises.
The Generating Function of Spanning Trees.
Exercises.
Partitions of an Integer.
Exercises.
A Generating Function for Solutions of Diophantine Systems in Nonnegative Integers.
Historical Notes.
References.
Classical Inversion.
Inversion in the Vector Space of Polynomials.
Taylor Expansions.
Exercises.
Formal Laurent Series.
Multivariate Laurent Series.
Exercises.
The Ordinary Generating Function.
Exercises.
The Gaussian Polynomials.
Exercises.
Notes.
References.
Graphs.
Cycles, Trails, and Complete Subgraphs.
Exercises.
Strongly Regular Graphs.
Exercises.
Spectra, Walks, and Oriented Cycles.
Index.