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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Divisions of space by parallels


Authors: G. L. Alexanderson and John E. Wetzel
Journal: Trans. Amer. Math. Soc. 291 (1985), 363-377
MSC: Primary 51M20; Secondary 05A19
DOI: https://doi.org/10.1090/S0002-9947-1985-0797066-2
MathSciNet review: 797066
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Abstract: An arrangement of hyperplanes in $ {\mathbb{E}^d}$ is a "plaid" provided its hyperplanes form no multiple flats of intersection and lie in parallel families that are in general position. We develop some geometrically natural formulas for the number of $ r$-faces that are formed by such an arrangement.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0797066-2
Keywords: Arrangements of hyperplanes, division of space, parallel hyperplanes, plaid, symmetric functions
Article copyright: © Copyright 1985 American Mathematical Society