Combinatorics Through Guided Discovery, 2004a

Index
S(k, n), 58
Π notation, 8
n!, 8
Stirling’s formula for, 19
n k , 55
n k , 8
q-ary factorial, 84
q-binomial coefficient, 84
s(k, n), 62
action of a group on a set, 115
arithmetic progression, 39
arithmetic series, 40
associative law, 105
asymptotic combinatorics, 36
automorphism (of a graph), 124, 131
basis (for polynomials), 61
Bell Number, 59
bijection, 11, 137
bijection principle, 11
binomial coefficient, 11
q-binomial, 84
Binomial Theorem, 24
binomial theorem
extended, 80
block of a partition, 6, 141
broken permutation, 57
Burnside’s Lemma, 123
Cartesian product, 5
Catalan Number, 22, 124
recurrence for, 89, 90
Catalan number
generating function for, 89
Catalan Path, 22
Cauchy-Frobenius-Burnside
Theorem, 123
characteristic function, 14
chromatic polynomial of a graph, 99
Chung-Feller Theorem, 23
closure property, 105
coefficient
multinomial, 60
coloring
standard notation, 117
standard ordering, 117
coloring of a graph, 98
proper, 98
combinations, 11
commutative law, 111
complement, 96
complement of a partition, 66
composition, 28, 137
k parts, 28
number of, 28
composition of functions, 104
compositions
number of, 28
congruence modulo n, 140
conjugate of an integer partition, 65
connected component graph, 165
connected component of a graph, 98,
165
connected structures and EGFs, 163
constant coefficient linear
recurrence, 40
contraction, 47
cost of a spanning tree, 46
cycle (in a graph), 43
cycle (of a permutation), 112
element of, 112
199