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Lattice Partitions with a Straight Line

Published online by Cambridge University Press:  20 November 2018

D. R. K. Brownrigg
D. R. K. Brownrigg*
Affiliation:
University of London, Goldsmiths' College
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Abstract

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In [1], the solution of a problem of distinct digital filter enumeration was expressed in terms of enumerating partitions of a rectangular set of lattice points with a straight line, under certain restrictions. Here, firstly, an explicit expression is derived for the number of such partitions in that and a more general case. Secondly, the asymptotic ratio of partitions to square of lattice dimensions is derived for a square lattice.

Keywords

05A1710A45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 3 , 01 September 1986 , pp. 287 - 294
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Brownrigg, D. R. K., The Weighted Median Filter, CACM, Vol. 27, No. 8, (1984), pp. 8–1984.Google Scholar
2. Hardy G., H., and Wright E., M., An Introduction to the Theory of Numbers, O.U.P. (1979).Google Scholar