HANDBOOK OF DISCRETE AND COMBINATORIAL MATHEMATICS

By X. BESIK

CONTENTS CHAPTER THE MATHEMATICS OF CHOICE 11 THE FUNDAMENTAL COUNTING PRINCIPLE 12 PASCAL’S TRIANGLE *13 ELEMENTARY PROBABILITY *14 ERROR-CORRECTING CODES 15 COMBINATORIAL IDENTITIES 16 FOUR WAYS TO CHOOSE 17 THE BINOMIAL AND MULTINOMIAL THEOREMS 18 PARTITIONS 19 ELEMENTARY SYMMETRIC FUNCTIONS *110 COMBINATORIAL ALGORITHMS CHAPTER THE COMBINATORICS OF FINITE FUNCTIONS 21 STIRLING NUMBERS OF THE SECOND KIND 22 BELLS, BALLS, AND URNS 23 THE PRINCIPLE OF INCLUSION AND EXCLUSION 24 DISJOINT CYCLES 25 STIRLING NUMBERS OF THE FIRST KIND PO´LYA’S THEORY OF ENUMERATION 31 FUNCTION COMPOSITION 32 PERMUTATION GROUPS 33 BURNSIDE’S LEMMA 34 SYMMETRY GROUPS 35 COLOR PATTERNS 36 PO´LYA’S THEOREM 37 THE CYCLE INDEX POLYNOMIAL GENERATING FUNCTIONS 41 DIFFERENCE SEQUENCES 42 ORDINARY GENERATING FUNCTIONS 43 APPLICATIONS OF GENERATING FUNCTIONS 44 EXPONENTIAL GENERATING FUNCTIONS 45 RECURSIVE TECHNIQUES ENUMERATION IN GRAPHS 51 THE PIGEONHOLE PRINCIPLE *52 EDGE COLORINGS AND RAMSEY THEORY 53 CHROMATIC POLYNOMIALS *54 PLANAR GRAPHS 55 MATCHING POLYNOMIALS 56 ORIENTED GRAPHS 57 GRAPHIC PARTITIONS CODES AND DESIGNS 61 LINEAR CODES 62 DECODING ALGORITHMS 63 LATIN SQUARES 64 BALANCED INCOMPLETE BLOCK DESIGNS