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 D+, n 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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