96 INDEX
matrix (cont.)
double staircase pattern, 91
doubly stochastic, 77
incidence, 39, 54
irreducible, 6, 14, 60, 61
L-matrix, 53
permanent, 49, 52
reducible, 6
sign pattern, 50, 55
potentially nilpotent, 56
SAP, 55
sign-nonsingular, 50
SNS, 50, 51
spectrally arbitrary, 55
signing, 52
simultaneous permutation, 2
skew-symmetric, 28
eigenvalues, 28
symmetric, 7
interlacing, 8
TNN, 90
totally nonnegative, 90
characterization, 92
totally positive, 90
weakly diagonally dominant, 59, 61
matroid, 25, 43, 70
basis, 25
circuit, 25
dependent set, 25
independent set, 25
rank, 25
rank function, 25
submodular inequality, 26
uniform, 25
minor monotone, 35
optimal assignment problem (OAP), 63
duality theorem, 64
Perron-Frobenius theory, 3
polytope
alternating sign matrix, 81
extreme points, 83
doubly stochastic, 78
extreme points, 78
qualitative class, 50
SDR, 26, 55
independent, 26, 43
spectral radius, 1, 2
square ice, 80
Strong Arnold Pproperty, 34
theorem
Ao-Hanson-Guidili-
arf´ as-Thomass´ e-Weidl, 72
Bassett-Maybee-Quirk, 51
Birkhoff, 78
Brauer-Gentry, 74
Brualdi-Kirkland, 88
Camion-Hoffman, 65
Colin de Verdi` ere, 35
de Boor-Pinkus, 91
Gale-Ryser, 41, 70, 72, 73
Gerˇ sgorin, 60
Graham-Pollak, 27
Kastelyn, 53
Kuratowski, 35
Landau, 69, 73
Lindstr¨ om-Tverberg, 54
McKay-Oggier-Royle-Sloane-Wanless-
Wilf,
88
Rado, 42
Rado-Hall, 26, 27, 55, 70, 78
Robertson-Seymour, 35
Schwarz, 3
Striker-Behrend-Knight, 81
Taussky, 61
Zeilberger, 80
tournament, 67
loss, 67
loss vector, 67
nearly regular, 74
regular, 74
score, 67
score vector, 67
transitive, 69, 71, 72
tournament matrix, 68
eigenvalues, 74
spectral radius, 75
transfer, 45
vector
support, 36
negative, 36
positive, 36
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