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Ryser H.J. — Combinatorial Mathematics
Ryser H.J. — Combinatorial Mathematics



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Название: Combinatorial Mathematics

Автор: Ryser H.J.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1963

Количество страниц: 166

Добавлена в каталог: 28.10.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$e^{-1}$      23
$n$-factorial      6
$n$-set      4
$r$-combination      7
$r$-permutation      5
$r$-sample      5
$r$-selection      7
$r$-subset      4
$\alpha$-width      77
$\alpha$-width, and finite planes      126 127
$\alpha$-width, maximal      77 127
$\alpha$-width, minimal      77
$\alpha$-width, of matrix $\tilde{A}$      77
($b$, $v$, $r$, $k$, $\lambda$)-configuration      96ff.
($b$, $v$, $r$, $k$, $\lambda$)-configuration, complement of      98
($b$, $v$, $r$, $k$, $\lambda$)-configuration, Fisher inequality for      99
($b$, $v$, $r$, $k$, $\lambda$)-configuration, incidence matrix of      97
($b$, $v$, $r$, $k$, $\lambda$)-configuration, isomorphic      98
($b$, $v$, $r$, $k$, $\lambda$)-configuration, necessary conditions for      97
($r_{1}, r_{2}, ..., r_{k}$) repartition      10
($v$, $k$, $\lambda$)-configuration      102ff.
($v$, $k$, $\lambda$)-configuration, and integral representations      118ff.
($v$, $k$, $\lambda$)-configuration, and maximal determinants      125
($v$, $k$, $\lambda$)-configuration, and permanents      124
($v$, $k$, $\lambda$)-configuration, conjectures on      111 124
($v$, $k$, $\lambda$)-configuration, incidence matrix of      102
($v$, $k$, $\lambda$)-configuration, nonexistence theorem for      111
Albert, A. A.      127
Array      see Rectangular array
Asymptotic formula      36
Bachet      1
Balanced incomplete block design      see ($b$
Baumert, L.      127
Berge, C.      59
bernoulli      19
Binomial coefficient      8
Binomial theorem      14
Block design      see ($b$
BLOCKS      96
Bose, R. C.      85 94 95 127 128
Brauer, A.      127 128
Bruck — Ryser Theorem      93 94 115
Bruck, R. H.      93 94 95 127 128 141
Bussey, W. H.      94 95
Chowla, S.      127 128
Circulant      123
Circulant, and difference sets      131
Circulant, conjecture on Hadamard      134
Circulant, in class $\mathcal{U}$($K$, $K$)      125
Class $\mathcal{U}$($K$, $K$)      77
Class $\mathcal{U}$($K$, $K$), circulants in      125
Class $\mathcal{U}$($K$, $K$), maximal permanent in      77
Class $\mathcal{U}$($K$, $K$), minimal permanent in      77 124
Class $\mathcal{U}$($R$,$S$)      61ff.
Class $\mathcal{U}$($R$,$S$), existence theorem for      63
Class $\mathcal{U}$($R$,$S$), interchange theorem for      68
Class $\mathcal{U}$($R$,$S$), normalized      69
Class $\mathcal{U}$($R$,$S$), number of matrices in      65
Collineation      123
Collineation, conjecture on      123
Column sum vector      61
Column sum vector, monotone      61
Combination      7
Combinatorial mathematics      2
Common representatives      see System of common representatives
Complement of ($b$, $v$, $r$, $k$, $\lambda$)-configuration      98
Complement of (0, 1)-matrix      98
Complete set      80
Complete set, and finite planes      92
Complete set, existence theorem for      81
Congruence of matrices      108
Congruence, of polynomials      136
Congruence, of quadratic forms      109
Conjecture of Euler      84ff.
Conjecture of van der Waerden      59 77 124
Conjecture on ($v$, $k$, $\lambda$)-configurations      111
Conjecture on collineations      123
Conjecture on convex $m$-gons      44
Conjecture on cyclic planes      132
Conjecture on distinct permanents      124
Conjecture on finite planes      94 123
Conjecture on Hadamard circulants      134
Conjecture on Hadamard matrices      106 115 122
Conjecture on integral representations      122
Conjecture on minimal permanents      124
Conjecture on multipliers      139
Connor, W. S.      128
Convex $m$-gon      43
Convex $m$-gon, conjecture on      44
Convex polygon      43
Coset      51
Coxeter, H. S. M.      130
Cyclic plane      132
Cyclic plane, conjectures on      132
Cyclic plane, of order      10 140
Da Silva      19
Dade, E. C.      127 128
Dance Problem      58
Degenerate submatrix      72
Degree of symmetric group      6
Derangement      22ff.
Desarguesian plane      132
Determinant      26
Determinant, Hadamard inequality on      105
Determinant, maximal      125
Dickson, L. E.      16 37
Difference set      see Perfect difference set
Direct product      106
Direct product, of Hadamard matrices      106
Direct sum      109
Disjoint sets      4
Distinct representatives      see System of distinct representatives
Dominoes      3
Doubly stochastic matrix      58
Doubly stochastic matrix, fundamental theorem on      58
Doubly stochastic matrix, van der Waerden conjecture on      59 77 124
Duality      90
Dulmage, A. L.      60 78
Eddington      7
Element      3
Enumeration problems      3
Eratosthenes      22
Erd$\ddot{o}$s, P.      36 37 46
Essential      1 71
Euler $\varphi$-function      20
Euler 36 officers problem      1 84
Euler conjecture      84ff.
Euler derangement recurrence      30
Euler square      see Orthogonal Latin Euler squares
Evans, T.      78
Evans, T. A.      141
Everett, C. J.      59
Existence problems      2
Extension of Latin rectangle      52 66
Ezra, Rabbi Ben      1
Feller, W.      16 28
Fibonacci number      30
Finite field      80
Finite projective plane      91ff.
Finite projective plane, and complete sets      92
Finite projective plane, and o-widths      126 127
Finite projective plane, Bruck — Ryser theorem on      93 94 115
Finite projective plane, conjecture on collineations of      123
Finite projective plane, conjecture on existence of      94
Finite projective plane, conjecture on uniqueness of      123
Finite projective plane, conjectures on cyclic      132
Finite projective plane, cyclic      132
Finite projective plane, cyclic of order      10 140
Finite projective plane, Desarguesian      132
Finite projective plane, equivalent postulates for      91
Finite projective plane, existence theorem for      93
Finite projective plane, nonexistence theorem for      93 94 115
Finite projective plane, number of      104
Finite projective plane, of order 10      94
Finite projective plane, order of      91
Finite projective plane, smallest      92
Finite set      4
Fisher inequality      99
Fisher, R. A.      128
Fixing of difference set      139
Ford, L. R., Jr      59 78
Fort, M. K., Jr      127 128
Four-square theorem      110
Fulkerson, D. R.      59 78
GaIois field      80
Gale, D.      78
Generalized rule of product      5
Generalized rule of sum      4
Gleason, A. M.      46
Goldberg, K      127 128
Goldhaber, J. K      127 128
Golomb, S. W.      127
Goodman, A. W.      46
Gordon, B.      141
Gordon, W. R.      127 129
Graeco-Latin square      see Orthogonal Latin squares
Greatest common divisor      19
Greenwood, R. E.      46
Group      6
Group, and coset decomposition      51
Group, as Latin square      36
Group, multiplier      136
Group, order of      7
Group, symmetric      6
Gruner, W.      127 128
Haber, R. M.      78
Hadamard configuration      107
Hadamard configuration, and difference sets      133
Hadamard inequality      105
Hadamard matrix      104ff.
Hadamard matrix, and integral representations      120 122
Hadamard matrix, conjecture on      106 115 122
Hadamard matrix, conjecture on circulants      134
Hadamard matrix, direct product of      106
Hadamard matrix, normalized      105
Hall, M., Jr      59 95 127 128 136 141
Hall, P.      48 59
Halmos, P. R.      59
Hanani, H.      127 128
Hardy, G. H.      28
Hedlund, G. A.      127 128
Higgins, P. J.      60
Hoffman, A. J.      60 129 141
Hughes, D. R.      129 141
Ideal line      93
Ideal point      93
Image      6
Incidence matrix      53ff.
Incidence matrix, of ($b$, $v$, $r$, $k$, $\lambda$)-configuration      97
Incidence matrix, of ($v$, $k$, $\lambda$)-configuration      102
Incidence matrix, permanent of      54 124
Incidence relation      89
Inclusion and exclusion formula      18
Integral representation      118ff.
Integral representation, and ($v$, $k$, $\lambda$)-configurations      118ff.
Integral representation, and Hadamard matrices      120 122
Integral representation, conjecture on      122
Integral representation, unsolved problem on      118
Interchange      67
Interchange theorem      68
Interchange, minimal number of      68
Interchange, theorem on      68
Intermediate term rank      70
Intersection of sets      4
Invariant 1, theorem on      69
Invariant o      69
Isbell, J. R.      129
Isomorphism of ($b$, $v$, $r$, $k$, $\lambda$)-configurations      98
Isomorphism of difference sets      135
Johnsen, E, C.      127 129
Jones, B. W.      127 129
K$\ddot{o}$nig, D      59 60
Kaplansky, I.      33 36 37
Kirkman triple system      101
Kirkman triple system, order of      101
Kirkman’s schoolgirls problem      1 101
Kleinfeld, E.      129
Kuhn, H. W.      60
Lagrange      110
Laplace expansion      26
Latin rectangle      35
Latin rectangle, asymptotic formula for      36
Latin rectangle, extension of      52 66
Latin rectangle, lower bound for      52 53
Latin rectangle, normalized      35
Latin rectangle, number of      36 37
Latin rectangle, square      36
Latin square      36
Latin square, order of      36
Latin square, orthogonal      79ff.
Latin square, unsolved problem on      67
Left coset decomposition      51
Legendre equation      114
Legendre theorem      114
Lehmer, E.      141
Line, ideal      93
Line, of matrix      55
Line, of projective plane      89
Line, ordinary      93
Lucas      32
M$\acute{e}$nage number      32ff.
M$\ddot{o}$bius function      21
MacNeish, H. F.      94 95
Magic square      1
Main diagonal      25
Majorization      62
Majumdar, K. N.      129
Mann, H. B.      59 60 94 95 129 141
Mapping      6
Mapping, image under      6
Mapping, into      6
Mapping, one to one      6
Mapping, onto      6
Mapping, product of      6
Marcus, M.      59 60 127 129
Matrix      25ff.
Matrix, circulant      123
Matrix, congruence of      108
Matrix, direct product of      106
Matrix, direct sum of      109
Matrix, doubly stochastic      58
Matrix, Hadamard      104ff.
Matrix, incidence      53ff.
Matrix, integral representation of      118
Matrix, maximal      62
Matrix, normal      103
Matrix, permutation      54
Matrix, quadratic form of      108
Matrix, zero-one      27 53ff. 61ff.
Maximal $\alpha$-width      77 127
Maximal determinant      125
Maximal matrix      62
Maximal permanent      77
Maximal term rank      70ff.
Maximal trace      76
Meaner, D. M.      128
Mendelsohn, N. S.      60 78
Mills, W. H      141
Mine, H.      60
Minimal $\alpha$-width      77
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