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                    Laywine C.F., Mullen G.L. — Discrete mathematics using Latin squares 
                  
                
                    
                        
                            
                                
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                                    Название:   Discrete mathematics using Latin squares 
Авторы:   Laywine C.F., Mullen G.L.  
Аннотация:  An intuitive and accessible approach to discrete mathematics using Latin squares In the past two decades, researchers have discovered a range of uses for Latin squares that go beyond standard mathematics. People working in the fields of science, engineering, statistics, and even computer science all stand to benefit from a working knowledge of Latin squares. Discrete Mathematics Using Latin Squares is the
 only upper-level college textbook/professional reference that fully engages the subject and its many important applications. Mixing theoretical basics, such as the construction of orthogonal Latin squares, with numerous practical examples, proofs, and exercises, this text/reference offers an extensive and well-rounded treatment of the topic. Its flexible design encourages readers to group chapters according to their interests, whether they be purely mathematical or mostly applied. Other features include: An entirely new approach to discrete mathematics, from basic properties and generalizations to unusual applications 16 self-contained chapters that can be grouped for custom use Coverage of various uses of Latin squares, from computer systems to tennis and golf tournament design An extensive range of exercises, from routine problems to proofs of theorems Extended coverage of basic algebra in an appendix filled with corresponding material for further investigation. Written by two leading authorities who have published extensively in the field, Discrete Mathematics Using Latin Squares is an easy-to-use academic and professional reference.
 
Язык:   
Рубрика:  Математика /Алгебра /Комбинаторика / 
Статус предметного указателя:  Готов указатель с номерами страниц  
ed2k:   ed2k stats  
Год издания:  1998 
Количество страниц:  326 
Добавлена в каталог:  11.03.2005 
Операции:  Положить на полку  |
	 
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                    Предметный указатель 
                  
                
                    
                        Latin square(s), partial        14   15    
Latin square(s), perfect        258   264    
Latin square(s), perfect, and conflict-free access to parallel memories        264    
Latin square(s), perfect, main subsquare        258    
Latin square(s), r-orthogonal        257   264    
Latin square(s), reduced        4     112   113   126    
Latin square(s), row        97—100   285    
Latin square(s), row complete        11   115   126    
Latin square(s), self-orthogonal        33   38   39   282    
Latin square(s), symmetric idempotent        13    
Latin square(s), transversals of        36   37    
Latin square(s), unipotent        112   113    
Lawrence, K.M.        244   250   251   254    
Laywine, C F.        27   37   39   45   51   61   62   70   71   146   152   164   169   170   173   174   253   254    
Lenz, H.        165   172   173    
Lewis, J.T.        226    
Lidl, R.        228   234   239   240   269   273   278    
Lindner, C.C.        124   128    
Lipschutz, S.        278    
Loops        97    
MacNeish's conjecture        26   27   37    
MacNeish, H.F.        26   27   37   40   58    
MacWilhams. F.J.        205   225   227    
Magic cube        291    
Magic squares        175—181   290    
Magic squares, 3-dimensional        180    
Magic squares, 3-dimensional, perfect        180    
Magic squares, addition-multiplication        179   180    
Magic squares, applications of        175    
Magic squares, defined        175    
Magic squares, multiplicative properties        181    
Magic squares, order        7      
Mahalanabis, A.        244   250   254    
Mandl, R.        18   37   40   263   265    
Mavron, V.C.        173   174    
McKay, B.D.        16   17   127   128    
Mead, R.        204    
Melencolia I        175   176    
Melliar-Smith, P.M.        259   264   266    
Menage numbers        86   90   91   93    
Menage problem        86—89   93    
Menage problem, enumeration of 3-row latin rectangles        93    
Mendelsohn, E.        124   128    
Mendelsohn, N.S.        124   128    
Mersenne primes        291    
Moebius inversion        93    
MOFS        see Mutually orthogonal frequency squares    
MOHC        see Mutually orthogonal hypercubes    
MOLS        see Mutually orthogonal latin squares    
Monte Carlo methods        253    
Montgomery, D.C.        204    
Moore, E.H.        20   38   40    
MOPLS        see Mutually orthogonal partial latin squares    
Moschopoulos, E.        175    
Moser, L.E.        259   264   266    
Mullen, G.L.        27   37—40   45   48   51   62   70   71   89   93   101   104   146   147   151   152   169   174   216   217   226   227   244   248—251   253   254     278    
Mullin, R.C.        171   173    
Multiplication (Cayley) table        95   103    
Mutually orthogonal frequency squares (MOFS)        64—70   284   288    
Mutually orthogonal frequency squares (MOFS), complete set        64    
Mutually orthogonal frequency squares (MOFS), construction by substitution        66—70    
Mutually orthogonal frequency squares (MOFS), nonconstant frequency        70    
Mutually orthogonal frequency squares (MOFS), polynomial construction        64—66    
Mutually orthogonal hypercubes (MOHC)        43—62   247—254   288   289   294    
Mutually orthogonal hypercubes (MOHC) and affine designs        153—173    
Mutually orthogonal hypercubes (MOHC), blocks        153   171   172    
Mutually orthogonal hypercubes (MOHC), complete set        51    
Mutually orthogonal hypercubes (MOHC), composition        153    
Mutually orthogonal hypercubes (MOHC), defined        44    
Mutually orthogonal hypercubes (MOHC), higher orthogonality        250—252    
Mutually orthogonal hypercubes (MOHC), Hoehler orthogonality        61    
Mutually orthogonal hypercubes (MOHC), MacNeish construction        57   58    
Mutually orthogonal hypercubes (MOHC), order        6     59    
Mutually orthogonal hypercubes (MOHC), polynomial construction        47—51   248    
Mutually orthogonal hypercubes (MOHC), recursive construction        51—57   61   249   250    
Mutually orthogonal hypercubes (MOHC), type        44    
Mutually orthogonal Latin squares (MOLS)        18—39   280—282   285   292   294    
Mutually orthogonal latin squares (MOLS) and Kronecker product        280   281    
Mutually orthogonal latin squares (MOLS), applications        18   37    
Mutually orthogonal latin squares (MOLS), complete set        20    
Mutually orthogonal latin squares (MOLS), deficiency of a set        33    
Mutually orthogonal latin squares (MOLS), defined        19    
Mutually orthogonal latin squares (MOLS), Desarguesian construction        21   22    
Mutually orthogonal latin squares (MOLS), Desarguesian set        22   35    
Mutually orthogonal latin squares (MOLS), isomorpbic sets        22   34    
Mutually orthogonal latin squares (MOLS), maximum number        19    
Mutually orthogonal latin squares (MOLS), nondesarguesian        146   147    
Mutually orthogonal latin squares (MOLS), nonisomorpbic sets        22    
Mutually orthogonal latin squares (MOLS), nonprime power sets        23   24    
Mutually orthogonal latin squares (MOLS), polynomial representation        20   21    
Mutually orthogonal latin squares (MOLS), power set of        35   36    
Mutually orthogonal latin squares (MOLS), prime power sets of        20   21    
Mutually orthogonal latin squares (MOLS), sets of nonisomorphk        280    
Mutually orthogonal partial latin squares (MOPLS)        255—257   264    
Mutually orthogonal partial latin squares (MOPLS), application to computer databases        256   257    
Mutually orthogonal partial latin squares (MOPLS), p-compatible        255    
Nets        293—295    
Niederreiter, H.        228   234   239   240   242—244   249   250   253   254   269   273   278    
Niven, I.        269   278    
Norton, D.A.        104   105    
Numerical integration        241   242   253    
One-way analysis of variance (ANOVA)        188   201    
Order, definitions of        102    
Orthogonal array(s)        31   32   36   37   197   246   247   280   281   294    
Orthogonal array(s), equivalent objects        31   32    
Orthogonal array(s), generalized        251    
Orthogonal hypercubes        see Mutually orthogonal hypercubes    
Orthogonal latin square graph (OLSG)        123—126    
Orthogonality, Hoehler's definition of        61    
Pairwise orthogonal squares        19    
Pandiagonal latin squares (Knut — Vik designs)        179    
Parker, E T.        8   17   26   37   39   40   101    
Partial latin square(s)        230     239    
Permutation cube(s)        43   223   224—226    
Permutation cube(s), reduced        224   225    
Permutation(s), theory of        95   96    
Perspective triangles        143—146    
Pilz, G.        269   278    
Piper, F.C.        152    
Plane(s), affine and projective        131—152    
Plane(s), desarguesian        172    
Plane(s), Euclidean        131   135   136   143    
Plane(s), Hall        146   147   151   172    
Pless, V.        225   227    
Poch, G.        263—265    
Polynomials, irreducible        272   273   277   278   280    
Posner, E.C.        213   216   226    
Preece, D.A.        264   265    
Prime power conjecture        38   152    
Prime power conjecture, Hoehler's partial resolution of for hypercubes        61   62    
Primes, Fermat        291    
Primes, Menenne        291    
Primitive element        274   277   291    
Principle of inclusion-exclusion        75—93    
Principle of inclusion-exclusion, defined        75   76    
Probert, R.L.        264—266    
Projective planes, axioms defining        138   139    
Projective planes, desarguesian        143—146   151    
Projective planes, Fano        150    
Projective planes, Hall        146   147   151    
Projective planes, Hughes        151    
Projective planes, incidence matrix        149   150    
Projective planes, incidence matrix, and duality principle        150    
Projective planes, nondesarguesian        146—150    
Projective planes, order of        139    
Projective planes, points at infinity        139   140    
Quad-groups        97    
Quadrangle criterion        97   104    
Quasi-Monte Carlo methods        253    
Raghavarao, D.        45   62   64   70   170   173    
Retkin, H.        102   104   105    
Ring, commutative        270    
Riordan, J.        90   93    
Rivest, R.L.        237—240    
Rogoyski, E.        16   17   127   128    
Rook polynomials        80—86   92   285    
Rook polynomials, defined        80   81    
Room squares        182—187   238   262    
Room squares and duplicate bridge tournaments        182   183   186    
Room squares, defined        182    
Room squares, Howell master sheets        182    
Room, T.G.        182—187    
Rota. G.-C.        93    
Row effects        190    
Row-latin square(s)        97—100    
Row-latin square(s), latin power set        99    
Row-latin square(s), orthogonal        98   99    
Row-latin square(s), power set        99    
Ryser. H.J.        38   39   93   152    
Salzburg, P.M.        263   265    
Sandier, R.        152    
Sarvate, D.G.        239   240    
Schmid, W.C.        250   251   254    
Schulz, R.-H.        263—265    
Seberry, J.        239   240    
Seiden, E.        45   62—64   70   170   173    
Shamir, A.        237—240    
Shiue, P.J.-S.        146   147   152    
Shrikhande, S.S.        8   17   26   33   37—40   101   172—174    
Simons, G.J.        230   239   240    
Simpson rule        241    
Singleton bound        212   221    
Siu, M.-K.        96   104   105    
Sloane, N.J.A.        205   225     244   254    
Smetaniuk, B.        15—17   230   239   240    
Smith, P.        58   62    
Sphere-packing (Hamming) bound        211   224    
Stinson, D.R.        8   17   37   40   117   128   263—265    
Straus, E.G.        58   62    
Street, A.P.        30   31   37   40   46   62   114   128    
Street, D.J.        30   31   37   40   46   62   114   128    
Suchower, S.J.        70   71   101   104   216   217   226   227    
Swiercz, S.        38   39    
Symmetric designs        155    
Tarry, G.        7   8   23   37    
Tay.T.-S.        257   264—266    
Thiel, L.        22   38   39   146   151   152    
Thompson, A.C.        181    
Three-orthogonality        229   243   251    
Tillson, T.W.        117   128    
Tismeneteky, M.        159   173    
Transversal design(s)        27—32   37    
Trapezoidal rule        241    
Two-way analysis of variance        189    
Uniform pseudorandom numbers        242    
Valeric M.        259   264   266    
van Lint, J.H.        39   40    
van Tilborg, H.C.A.        228   239   240    
Vaughan, H.E.        109   128    
Vector spaces        274—278    
Vector spaces and error-corrrecting codes        276   277    
Vector spaces, addition of vectors        274    
Vector spaces, examples of        275   276    
Vector spaces, finite-dimensional        276    
Vector spaces, finite-dimensional, dimension of        276    
Vector spaces, scalar multiplication        274    
Vector spaces, sets of vectors        276    
Vector spaces, sets of vectors, linear combination        276    
Vector spaces, sets of vectors, linearly dependent        276   277    
Vector spaces, sets of vectors, linearly independent        276   277    
Vector spaces, sets of vectors, spanning        276    
Vector spaces, subspaces        276—277    
Wallis, W.D.        172   174   186   187    
Wan, D.        146   147   152    
Weber, R.E.        226   227    
Whittle, G.        27   37   39   45   51   62   248   249   253   254    
Williams, A.W.        264—266    
Williams, E.J.        116   128    
Wilson's problem        39    
Wilson, R.M.        39   40    
Wolk, B.        124   128    
Yamamoto, K        91   93    
Yates, F.        204    
Zuckerman, H.S.        269   278    
                            
                     
                  
			 
		          
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