158 INDEX
Minkowski
conjecture, 128
critical value, 25
geodesic MCF, 25
reduction, 19
’s algorithm, 20
’s second fundamental theorem, 22
lexicographical reduced, 25
Minkowski-Hlawka, 9
moduli space, 37
moment of inertia, 97
Mordell type inequality, 54
Morse function, 128
m-perfect, 40
m-periodic (point) set, 37
norm, 5
normal cone, 29
normalizer, 50
number field
Euclidean , 111
thin , 111
totally real , 110
weakly thin , 111
open
polyhedral subdivision, 51
ray, 3
oriented matroid, 62
orthogonal complement, 42
outer
coefficient, 4
normal cone, 94
packing radius, 6, 9
packing-covering
constant, 13
optimizer, 90
problem, 13
locally optimal lattice , 84
parallelotope, 5
partial quotient matrices, 24
partition backtrack, 136
patchwork lattice, 49
perfect
strongly , 44
perfect Delone polytope, 75
perfect form, 29
contiguous , 30
Eisenstein , 52
Gaussian , 53
Hurwitz quaternionic , 54
Voronoi’s first , 31
periodic extreme set, 43
periodic form, 37
periodic set, 10, 27
m-∼ , 37
rational , 46
standard , 37
pessimum, 12, 126
point density
upper, lower , 9
polyhedral
complex, 75, 133
subdivision, 35
polyhedral cone, 132
automorphism group of , 74
GLt
d
(Z)-equivalent , 74
rational normalized , 73
polyhedron, 131
locally finite , 28
vertex-set of , 60
polytope, 132
Gosset , 75, 126
regular cross , 127
repartitioning , 69
Schl¨ afli , 75, 126
secondary , 57
positive
definite quadratic form, 2
semidefinite quadratic form, 4
PQF (see also under quadratic form), 2
principle congruence subgroup, 46
projective automorphism group, 134
quadratic form, 1
rigid, 114
adjoint , 35
characteristic , 73
Eisenstein , 52
E-perfect , 52
eutactic , 34
extreme , 34
Gaussian , 53
GLt
d
(Z)-equivalent , 48
G-perfect , 49
G-perfect , 53
(G, t)-perfect , 49
H-perfect , 54
Hurwitz quaternionic , 53
Minkowski reduced , 19
perfect , 29
positive definite , 2
positive semidefinite , 4
rank-1 , 29
rational, real, integral , 1
reduced , 17
strongly eutactic , 43
strongly perfect , 44
t-eutactic , 47
t-extreme , 47
T -perfect , 49
t-perfect , 47
(T, t)-perfect , 49
quantizer problem, xv
randomized algorithm, 72
rank-1 form, 29
Previous Page Next Page