A Helly-type theorem for intersections of orthogonally starshaped sets in \mathbb R^d |
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Authors: | Marilyn Breen |
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Institution: | 1. Department of Mathematics, University of Oklahoma, Norman, OK, 73019, USA
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Abstract: | Let $\mathcal K$ be a finite family of orthogonal polytopes in $\mathbb R^d$ such that, for every nonempty subfamily $\mathcal K^\prime $ of $\mathcal K, \cap \{K : K$ in $\mathcal K^\prime \}$ , if nonempty, is a finite union of boxes whose intersection graph is a tree. Assume that every $d + 1$ (not necessarily distinct) members of $\mathcal K$ meet in a (nonempty) staircase starshaped set. Then $S \equiv \cap \{ K : K$ in $\mathcal K\}$ is nonempty and staircase starshaped. |
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