Letter | Published:

Random Association of Points on a Lattice

Nature volume 162, page 333 (28 August 1948) | Download Citation



A LATTICE is defined to be a rectangular array of points each of which may be any one of k colours. In a previous communication1, I have given the first and the second moments for the probability distribution of the total number of joins between points of different colours, when the probability that any point is of colour r and is Prk1Pr=1)and is independent of the colour of all the other points. A join was there defined as a line between two adjacent points parallel to the axes of the lattice. The present note gives the first and the second moments for the distribution of (1) the number of joins between points of the same colour, and (2) the total number of joins between points of different colours for two- and three-dimensional lattices when all possible joins between adjacent points are included. The first distribution corresponds to Todd‘s distribution of “doublets”2.

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  1. 1.

    , Nature, 160, 714 (1947).

  2. 2.

    , J. Roy. Stat. Soc. Suppl., 7, 78 (1940).

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  1. Department of the Design and Analysis of Scientific Experiment, Oxford. April 9.



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