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Rectangulations

Published online by Cambridge University Press:  24 October 2008

Norman Biggs
Affiliation:
University of Southampton

Extract

The subject of squared rectangles and squared squares was developed by Brooks, Smith, Stone and Tutte(1) using techniques based on the theory of electrical networks. In this note we shall treat the (apparently) more general topic of rectangulations using purely algebraic techniques. The starting point is the observation that the incidence matrices of the pair of dual networks associated with a squared rectangle in (l) can be more naturally derived as incidence matrices of the squaring (or rectangulation) itself. Further, the topological information contained in the networks is a simple consequence of Euler's formula applied directly to the rectangulation.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCE

(1)Brooks, R. L., Smith, C. A. B., Stone, A. H. and Tutte, W. T.The disection of rectangles into squares. Duke. Math. J. 7 (1940), 312340.CrossRefGoogle Scholar