عنوان

Introduction to combinatorics

Introduction to combinatorics

xli, 230 pages : illustrations ; 25 cm.

Wiley series in discrete mathematics and optimization ;87

Bibliographical references )pages 223-224( and index

Martin J. Erickson, Department of Mathematics and Computer Science, Truman State University, Kirksville, MO

1

Machine generated contents note: Preface xi1 Basic Counting Methods 11.1 The multiplication principle 11.2 Permutations 14.3 Combinations 16.4 Binomial coefficient identities 101.5 Distributions 191.6 The principle of inclusion and exclusion 132.7 Fibonacci numbers 113.8 Linear recurrence relations 133.9 Special recurrence relations 114.01 Counting and number theory 54Notes 205 Generating Functions 235.1 Rational generating functions 235.2 Special generating functions 236.3 Partition numbers 267.4 Labeled and unlabeled sets 208.5 Counting with symmetry 268.6 Cycle indexes 239.7 Polya's theorem 269.8 The number of graphs 289.9 Symmetries in domain and range 2201.01 Asymmetric graphs 301Notes 3501 The Pigeonhole Principle 3701.1 Simple examples 3701.2 Lattice points, the Gitterpunktproblem, and SET)r( 3011.3 Graphs 3511.4 Colorings of the plane 3811.5 Sequences and partial orders 3911.6 Subsets 421Notes 4621 Ramsey Theory 4131.1 Ramsey's theorem 4131.2 Generalizations of Ramsey's theorem 4531.3 Ramsey numbers, bounds, and asymptotics 4931.4 The probabilistic method 4341.5 Sums 4541.6 Van der Waerden's theorem 641Notes 5051 Codes 5351.1 Binary codes 5351.2 Perfect codes 5651.3 Hamming codes 5851.4 The Fano Configuration 261Notes 6861 Designs 6171.1 t-designs 171CONTENTS ix6.2 Block designs 6571.3 Projective planes 6081.4 Latin squares 6281.5 MOLS and OODs 6581.6 Hadamard matrices 6881.7 The Golay code and S)5, 8, 42( 6491.8 Lattices and sphere packings 6791.9 Leech's lattice 991Notes 102A Web Resources 502B Notation 702Exercise Solutions 112References 522Index 722

، Combinatorial analysis

، MATHEMATICS / Discrete Mathematics

3691-

Erickson, Martin J.

AU

TI

SE