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Index
Addition rule 2
anagram 18
antiarithmetic sequence 139
Appel, K. 275
arithmetic sequence 136
arrangement 109
of n elements 6
with repetitions 17
array 143
ascending integer 31
strictly 32
attainability problem 193
auxiliary colorings 281
balanced partition 180
Bernoulli's inequality 327
Bezout's theorem 351
bijection 96
bijection rule 6, 56
binomial coefficient 11
boundary 242
conditions 24
point 242
bounded region 242
Burnside's lemma 97
Cartesian
coordinates 62
product 4
Cayley's problem 230
checkerboard 269
chessboard 269
class of a partition 175
classical combinatorics 1
collinear points 220
coloring 273
of chessboards 277
of points 273
of regions 275
column sum 143
combination
with repetitions 20
without repetitions 11
combinatorial
geometry 217
number 11
planimetry 218
topology 218
combinatorics, classical 1
configurations, numerical 107
connected set 242
convex
body 219
390
Index
convex (continued)
hull 219
polygon 219
counting
intersections 222
polygons 230
triangles 225
covering 257
curve 242
cyclic sequence 122
geometric sequence 136
graph 133
planar 275
decimal system 29
digit representation 79
Diophantine equation 33
direct construction 107
Dirichlet's principle 2, 5, 33, 107
Dirichlet's theorem 138
discrete geometry 218
distributions into bins 76
dividing space 255
dividing the plane
with a system of lines 243
with closed curves 246
divisibility 109
dodecahedron 100
domino 269
identity permutation 82
inclusion-exclusion principle 2, 66,
258
generalization 89
infinite sequence 121
interior point 242
invariant 196
iteration 192
equivalence relation 96
Euler's ip-function 86
extremal problem 108
Fibonacci
numbers 330
sequence 187
finite sequence 121
finiteness problem 193
fixed point 82
four-color problem 273
function
Euler's 86
Mobius 87, 361
onto 75
general position
of lines 244
of planes 255
generalized diagonal 154
Hadwiger, Hugo 218
Haken, W. 275
Hasse diagram 115
Heawood's theorem 276
Heawood, P.J. 275
Helly's theorem 237
Jordan's theorem 238
Jung's theorem 260
k-combination 11
length of a sequence 121
line bundle 222
linear ordering 115
mapping 192
mathematical induction 107
matrix 143
method of
auxiliary coloring 281
construction 107
extremes 108, 232
invariants 196
parallels 229
words 56
Mobius
function 87, 361
inversion formula 87
multiplication rule 2, 3
multiplicity 17
multiset 16
Index
Newton's theorem 354
nonconvex polygon 238
number of divisors 89
numerical configurations 107
onto function 75
open set 242
optimization 217
ordered k-tuple 1
overlapping 257
packing 257
parity-balanced sequence 132
partially ordered set 115
partition
of a set 174
cardinality-balanced 180
sum-balanced 180
Pascal's triangle 160
perfect power 139
periodicity problem 193
permutation 8, 82
pigeonhole principle 2, 5, 107
planar graph 275
P6lya's theory of enumeration 95
polygon 238
convex 219
nonconvex 238
principle
Dirichlet's 2, 5, 33, 107
inclusion exclusion 2, 66, 258
pigeonhole 2, 5, 107
problem
attainability 193
Cayley's 230
extremal 108
finiteness 193
four-color 273
periodicity 193
stabilization 193
Sylvester's 232
product of divisors 89
recursive
construction 107
method 103
region 242
;{91
bounded 242
unbounded 242
relation 192
Riemann, Bernhard 217
row sum 143
rule
addition 2
bijection 6
multiplication 2, 3
sequence 121
antiarithmetic 139
arithmetic 136
cyclic 122
Fibonacci 187
geometric 136
infinite 121
nondecreasing 22
parity-balanced 132
set
open 242
partially ordered 115
partition of 174
stabilization problem 193
Stirling numbers of the second kind
78
subarray 148
subgroup 97
subsequence 127
subsets 11
sum of divisors 89
Sylvester's problem 232
tetromino 269
Thales circle 364
theorem
Bezout's 351
Dirichlet's 138
Reawood's 276
Reily's 220
Jordan's 238
Jung's 260
Newton's 354
van der Waerden's 174
theory of convex sets 218
tilings 218, 257
triangular array 160
tromino 269
392
Index
unbounded region 242
valuation 203
van der Waerden's theorem 175
variation
with repetitions 13
without repetitions 8
vertex of a polygon 220
walks in rectangular grids 62
words 60
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