Abstract
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 Pr(Σk1Pr=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.
Similar content being viewed by others
Article PDF
References
Krishna Iyer, P. V., Nature, 160, 714 (1947).
Todd, H., J. Roy. Stat. Soc. Suppl., 7, 78 (1940).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
IYER, P. Random Association of Points on a Lattice. Nature 162, 333 (1948). https://doi.org/10.1038/162333b0
Issue Date:
DOI: https://doi.org/10.1038/162333b0
This article is cited by
-
Runs in a Sequence of Observations
Nature (1951)
-
Variance of Triplets
Nature (1949)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.