Abstract
Design Theory, a branch of mathematics, was born out of the experimental statistics research of the population geneticist R A Fisher and of Indian mathematical statisticians in the 1930s. The field combines elements of combinatorics, finite projective geometries, Latin squares, and a variety of further mathematical structures, brought together in surprising ways. This essay will present these structures and ideas as well as how the field came together, in itself an interesting story.
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References
Baez J C 2001 The Octonions; Bull. New Ser., Am. Math. Soc. 39 145–205 and www.jmath.usr.edu/home/baez/octonions
Bennett C H and Brassard 1984 Proceedings of the IEEE Conference on Computers, Systems and Signal Processing, Bangalore, India (New York: IEEE) pp 175–179
Bennett J H 1983 Natural selection, heredity, and eugenics (Oxford: Clarendon Press)
Beth T, Jungnickel D and Lenz H 1985 Design Theory (Zürich: Bibl. Inst.) and 1993 Encyclopedia of mathematics (Cambridge: Cambridge University Press) vol. 69
Biggs N L 1981 T P Kirkman, mathematician; Bull. London Math. Soc. 13 97–120
Biggs N L 1985 Discrete mathematics (Oxford: Clarendon Press)
Bose R C 1939 On the construction of balanced incomplete block designs; Ann. Eugenics 9 353–399
Bose R C and Manvel B 1984 Introduction to combinatorial theory (New York: John Wiley Press)
Bose R C, Parker E T and Shrikhande S 1960 On orthogonal Latin squares; Can. J. Math. 12 189–203
Box Joan Fisher 1978 R. A. Fisher: The Life of a Scientist (New York: John Wiley Press)
Coxeter H S M 1946 Integral Cayley Numbers; Duke Math. Journal 13 561–578
Dickson L E 1919 On quaternions and their generalization and the history of the eight square theorem; Ann. Math. 20 155–171
Dixon G M 1994 Division algebras: Octonions, quaternions, complex numbers and the algebraic design of physics Vol. 290 Mathematics and its Applications (Dordrecht: Kluwer Press)
Ekert A 1991 Quantum cryptography based on Bell’s theorem; Phys. Rev. Lett. 67 661–663
Fienberg S E and Hinkley D V 1980 R.A. Fisher: An appreciation Lecture Notes in Statistics 1 (New York: Springer)
Fisher R A 1930 The genetical theory of natural selection (Oxford: Oxford University Press)
Fisher R A 1935 The design of experiments (Edinburgh: Oliver and Boyd)
Fisher R A 1940 An examination of the different possible solutions of a problem in incomplete blocks; Ann. Eugenics 10 52–75
Fisher R A 1941/2 New cyclic solutions to problems in incomplete blocks; Ann. Eugenics 11 290–299
Fisher R A and Yates F 1949 Statistical tables for biological, agricultural and medical research 3rd edition (London: Oliver and Boyd)
Gani J 1982 The making of statisticians (Berlin: Springer-Verlag)
Gropp H 1991 The history of Steiner systems S(2,3,13); Mitteilungen Math. Gesellschaft Hamburg 12 849–861
Gropp H 1992 The birth of a mathematical theory in British India; Colloq. Math. Soc. Janos Bolyai 60 315–327
Hadamard J 1893 Resolution d’une question relative aux determinants; Bull. Sci. Math. 2 240–246
Hall M Jr 1967 Combinatorial theory (Waltham, MA: Blaisdell Press)
Hankins T L 1980 Sir William Rowan Hamilton (Baltimore: Johns Hopkins University Press)
Hirschfeld J W P 1979 Projective geometries over finite fields (Oxford: Oxford University Press)
Hughes D R and Piper F C 1985 Design theory (Cambridge: Cambridge University Press)
Jungnickel D 1990 Latin squares, their geometries and their groups. A survey; in Coding Theory and Design Theory Part II Design theory (ed.) D Ray-Chaudhuri (vol 21 of the IMA Volumes in Math. and its Appl.) (Berlin: Springer) pp 166–225
Kirkman T P 1847 On a problem in combinations; Cambridge Dublin Math. J. 2 191–204
Kirkman T P 1850 Query VI; Lady’s and Gentleman’s Diary 147 48 and Note on an unanswered prize question; Cambridge Dublin Math. J. 5 255–262
Lenz H 1991 Half a century of Design Theory; Mitteilungen Math. Gesellschaft Hamburg 12 579–593
Levay P, Saniga M and Vrana P 2008 Three-qubit operators, the split Cayley hexagon of order two and black holes; Phys. Rev. D 78 124002 (1–22)
Pinl M 1971/2 Kollegen in einer dunklen Zeit, III Teil; Jahresber. Dtsch. Math.-Vereinigung 73 153–208
Planat M and Saniga M 2008 On the Pauli graphs on N-qudits; Quantum Inf. Comput. 8 127–146
Rao Raghava D 1971 Constructions and combinatorial problems in design of experiments (New York: John Wiley Press)
Rau A R P 2009a Algebraic characterization of X-states in quantum information arXiv:0906.4716
Rau A R P 2009b Mapping two-qubit operators onto projective geometries; Phys. Rev. A 79 042323 (1–6)
Reiss M 1859 Über eine Steinerische combinatorische Aufgabe; J. Reine Angew. Math. 56 326–344
Savur S R 1939 A note on the arrangement of incomplete blocks, when k = 3 and λ = 1; Ann. Eugenics 9 45–49
Steiner J 1853 Combinatorische Aufgabe; J. Reine Angew. Math. 45 181–182
Tankard J W Jr 1984 The statistical pioneers (Cambridge: Schenkman Publishing)
Witt E 1938 Über Steinerische Systeme; Abh. Hamburg 12 265–275
Woolhouse W S B 1844 Prize Question 1733; Lady’s and Gentleman’s Diary
Yates F 1936 Incomplete randomized blocks; Ann. Eugenics 7 121–140
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Rau, A.R.P. R A Fisher, design theory, and the Indian connection. J Biosci 34, 353–363 (2009). https://doi.org/10.1007/s12038-009-0041-3
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DOI: https://doi.org/10.1007/s12038-009-0041-3