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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Illumination for unions of boxes in $\textbf {R}^ d$
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by Marilyn Breen PDF
Proc. Amer. Math. Soc. 116 (1992), 197-202 Request permission

Abstract:

Let $S$ be a finite union of boxes (polytopes whose edges are parallel to the coordinate axes) in ${R^d}$. If every two vertices of $S$ are clearly illumined by some common translate of the box $T$, then there is a translate of $T$ that clearly illumines every point of $S$ . A similar result holds when appropriate boundary points of $S$ are illumined (rather than clearly illumined) by translates of box $T$.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 197-202
  • MSC: Primary 52A30
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1089402-6
  • MathSciNet review: 1089402