Combinatorial theory and statistical design
著者
書誌事項
Combinatorial theory and statistical design
（Wiley series in probability and mathematical statistics, . Probability and mathematical statistics）
Wiley, c1987
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注記
Includes bibliographies and index
内容説明・目次
内容説明
This balanced and comprehensive treatment of topics in discrete mathematics and statistical design raises new questions and assesses potential difficulties surrounding various techniques. A broad range of topics is covered, from counting and enumeration techniques to graphs and networks, combinatorial and statistical designs and partially ordered sets. The book 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 examined are 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.
目次
- Ways to Choose
- The Essentials of Counting
- Occupancy
- More on Counting
- Historical Notes
- Generating Functions
- The Formal Power Series
- The Combinatorial Meaning of Convolution
- Generating Functions for Stirling Numbers
- Bell Polynomials
- Recurrence Relations
- The Generating Function of Spanning Trees
- Partitions of an Integer
- A Generating Function for Solutions of Diophantine Systems in Nonnegative Integers
- Historical Notes
- Classical Inversion
- Inversion in the Vector Space of Polynomials
- Taylor Expansions
- Formal Laurent Series
- Multivariate Lauren Series
- The Ordinary Generating Function
- The Gaussian Polynomials
- Graphs
- Cycles, Trails and Complete Subgraphs
- Strongly Regular Graphs
- Spectra, Walks and Oriented Cycles
- Index.
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