364 Index
distortion, 243
duality
gap, 165, 168
of
L1
and
L∞,
155
of continuous functions and signed mea-
sures, 155
of Euclidean spaces, 155
of spaces of symmetric matrices, 155
of topological vector spaces, 159
of vector spaces, 154
strong, 173
edge, 252
ellipsoid, 203
center of, 203
maximum volume, 209
minimum volume, 209, 216
Euler characteristic, 29, 31
Eulerian numbers, 269
extreme ray, 65
face, 50
figure, 253
proper, 50
facet, 252
Farkas Lemma, 174
feasible flow, 61
forest, 63
Formula
double precision, 71
Euler-Poincar´ e, 259
Gauss-Bonnet, 261
Inclusion-Exclusion, 28
Pick’s, 291
Stirling’s, 297
Fourier-Motzkin elimination, 38
function
Gamma, 297
generating, 325
indicator, 6, 28
Lov´ asz’s theta, 182
support, 36, 207
graph
d-realizable, 94
chordal, 97
realizable, 94
Grassmannian, 36, 246
halfspace
closed, 23, 43
open, 23, 43
hyperoctahedron, 9
hyperplane, 21, 42
dense, 112, 113
isolating, 44
strictly, 44
separating, 44
strictly, 44
support, 50
identity
Fleck’s, 14
Liouville’s, 14
index of a vertex, 267
inequality
active, 54
Brunn-Minkowski, 206, 234
functional, 206
concentration
for Lipschitz functions, 237, 247
for the Gaussian measure, 236
for the unit sphere, 247
Firey, 207
isoperimetric
for the Gaussian measure, 234
for the sphere, 246
interior, 47, 111
algebraic, 109
interval, 2, 5
kissing number, 304
lattice, 280
Ad, 280
Dn, 281
Dn +, 281
E6, 281
E7, 281
E8, 281
basis of, 280
fundamental parallelepiped of, 286
reduced, 319
covering radius of, 311
determinant of, 287
dual, 309
fundamental parallelepiped of, 286
packing density of, 302
packing radius of, 302
rank of, 280
standard integer, 280
unimodular, 288
linear functional, 42
positive, 134, 161, 197
map
continuous, 110
moment, 4
rigidity, 98
matrix
r-diagonal, 93, 181
doubly stochastic, 56
Gram, 94
permutation, 56
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