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Online Encyclopedia
Originally appearing in Volume V06, Page 758 of the 1911 Encyclopedia Britannica.
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DP1DP 2 ... DP n hA l hx z ... lr7 m Putting as before Al=3, X2=2, X3=1, p1=2, p2=2, p3=1, pa=I, the reader will have no difficulty in constructing the diagrams of the eighteen solutions. The next and last example of a multitude that might be given shows the extraordinary power of the method by solving the famous problem of the " Latin Square," which for hundreds of years had proved beyond the powers of mathematicians. The problem consists in placing n letters a, b, c,...n in the compartments of a square lattice of n2 compartments, no compartment being empty, so that no letter occurs twice either in the same row or in the same column. The function is here Fi0.2n—10.2n—2...20. n' 1 2 _10.11 I and the operator Dn , the enumeration being given by 2 -1 D n 2n—1 2n—2 ' 2 n 2n-I(Ea a .. a and 1 n-1 See Trans. Comb. Phil. Soc. vol. xvi. pt. iv. pp. 262-290.
End of Article: DP1DP 2

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