Carrying on with within the bestselling, informative culture of the 1st version, the Handbook of Combinatorial Designs, moment Edition is still the one source to comprise all the most vital effects and tables within the box of combinatorial layout. This guide covers the structures, homes, and purposes of designs in addition to lifestyles results.
Over 30% longer than the 1st version, the booklet builds upon the basis of its predecessor whereas keeping the unique individuals' services. the 1st half encompasses a short advent and historical past of the topic. the subsequent elements specialize in 4 major periods of combinatorial designs: balanced incomplete block designs, orthogonal arrays and Latin squares, pairwise balanced designs, and Hadamard and orthogonal designs. heavily hooked up to the previous sections, the subsequent half surveys sixty five extra periods of designs, akin to balanced ternary, factorial, graphical, Howell, quasi-symmetric, and round. the ultimate half offers mathematical and computational historical past concerning layout theory.
New to the second one Edition
Meeting the necessity for up to date and obtainable tabular and reference info, this guide offers the instruments to appreciate combinatorial layout thought and functions that span the whole discipline.
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Additional info for Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
1. . . 484} lim = 484, [2159, 1338, 289, 753], Theorem four. sixteen. {m = 2n, 1 ≤ n ≤ 484} ∪ {3} ∪ {m = 6n + three, three ≤ n ≤ a hundred and sixty} ∪ {969} lim = 969, [1783, 289], Theorems four. sixteen, four. 18. {1,2, four. . . 322} lim = 323, [289, 753], Theorem four. sixteen. {2,4. . . 323} lim = 323, [289, 753], Theorem four. sixteen. List(5, 12, 24) lim = 4199. {1. . . nine} lim = nine, Theorem four. eight. {1. . . 28} lim = 28, Theorem four. eight. {1. . . 484} lim = 484, Theorem four. sixteen. {1,2, 6. . . 233} lim = 323, Theorems four. eight, four. sixteen. {2,4. . . 323} lim = 323, Theorems four. eight, four. sixteen. List(5, eleven, 24)∪List(5, 12, 25)∪List(5, eleven, 25) lim = 323, Theorem four. sixteen. List(5, 12, 24)) lim = 4199, Theorem four. sixteen. {1, 2, three} lim = three, Theorem four. 20. {1} lim = 1, [1352]. (See instance four. 21. ) {1} lim = 1, [333]. {2, three} lim = three, Theorems four. 20, four. 18. {1} lim = 1, [2069]. {3, four, five} lim = five, D16 , [333], Theorem four. sixteen. {3, four, five} lim = five, HOL(C16 ), HOL(C8 ) × C2 , [333]. {4. . . sixteen} lim = sixteen, Theorem four. 20. {2. . . five} lim = five, [333, 2069]. {3, four, five} lim = five, [2069, 1333]. {4, five, 6} lim = 6, [333, 1333], Theorem four. sixteen. {1. . . 6} lim = 6, [1333]. 88 t-Designs with t ≥ three 5-(18, eight, m2) 5-(18, nine, m5) 5-(19, 6, m2) 5-(19, 7, m7) 5-(19, eight, m28) 5-(19, nine, m7) 5-(20, eight, m35) 5-(20, nine, m105) 5-(20, 10, m21) 5-(21, 6, m4) 5-(21, 7, m30) 5-(21, eight, m280) 5-(21, nine, m70) 5-(21, 10, m168) 5-(22, 6, m) 5-(22, 7, m2) 5-(22, eight, m20) 5-(22, nine, m70) 5-(22, 10, m14) 5-(22, eleven, m28) 5-(23, 6, m6) 5-(23, 7, m3) 5-(23, eight, m8) 5-(23, nine, m90) 5-(23, 10, m252) 5-(23, eleven, m42) 5-(24, 6, m) 5-(24, 7, m3) 5-(24, eight, m) 5-(24, nine, m6) 5-(24, 10, m18) 5-(24, eleven, m42) 5-(24, 12, m6) II. four {3, 7, eight, 15, sixteen, 20, 22, 23, 24, 30. . . 33, 38. . . forty-one, forty six. . . forty nine, fifty two, fifty four. . . fifty seven, sixty two. . . sixty five, 70, seventy one} lim = seventy one, [1333, 1504], Theorems four. 18, four. sixteen. {3, 6. . . seventy one} lim = seventy one, [333, 1333], Theorems four. sixteen, four. 20. {2, three} lim = 7, HOL(C19 ) [239]. {4, five, 6} lim = 6, [333, 2069], Theorem four. 18. {2. . . 6} lim = 6, [2069], Theorem four. sixteen. {3, 7, eight, 15, sixteen, 18 . . . seventy one} lim = seventy one, PSL(2, 17)+, [333, 1320, 2069], Theorem four. sixteen. {1. . . 6} lim = 6, [1337]. {1. . . 6} lim = 6, [1337, 2069]. {3, 6. . . seventy one} lim = seventy one, [1337], Theorems four. 18, four. 20. {1, 2} lim = 2, HOL(C21 ), Theorem four. sixteen. {2} lim = 2, Theorem four. sixteen. {1} lim = 1, Theorem four. sixteen. {2. . . 6, eight. . . thirteen} lim = thirteen, PSL(2, 19)+, Theorem four. sixteen, PSL(3, 2) × S3 , (PΓL(2, nine) × id2 )+ [2069]. {2, four, five, 6, eight, 10, eleven, 12, thirteen} lim = thirteen, PGL(2, 19)+, PSL(3, 2) × S3 , [1335, 2069], Theorem four. 18. {4. . . eight} lim = eight, Theorem four. sixteen. {8, sixteen, 18, 20, 24, 28, 30, 34} lim = 34, Theorems four. sixteen, four. eight. {2. . . 12, 14, sixteen, 17} lim = 17, PSL(2, 19)++, Theorem four. eight. {3, four, 6, 7, nine, 10, 12, thirteen, 15, sixteen, 17} lim = 17, PSL(2, 19)++, Theorem four. sixteen. List(6, eleven, 23) ∪ {18, 22, 27, 28, 30, 33, 34, 37, 39, forty, forty two, forty three, forty four, forty five, forty eight, forty nine, fifty two, fifty four, fifty seven, fifty eight, 60, sixty eight, sixty nine, 70, seventy five, eighty four, 88, ninety three, ninety six, ninety seven, 102, one hundred ten, 124, 129, 136, 138, 142, a hundred and seventy, 174, 183, 202, 221} lim = 221, M11 × C2 , PSL(2, 19)++, PSL(3, four) − ⊕C2, PΓL(2, nine) × C2 ⊕ C2 , Theorems four. 18, four. sixteen. List(4, 10, 21) lim = 221, Theorem four. 20. {1} lim = 1, HOL(C23 ). {12, 15, 18, 21, 24} lim = 25, Theorem four. sixteen. {12, 24, 27, 30, 36, forty eight, fifty one} lim = fifty one, Theorems four. eight, four. 18, four. sixteen. {3, four, 6, 7, nine, 10, eleven, thirteen, sixteen, 17} lim = 17, Theorems four.