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Breen, Marilyn

Sets expressible as unions as staircase \(n\)-convex polygons. (English) Zbl 1244.52009

Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 50, No. 1, 23-28 (2011).
Summary: Let \(k\) and \(n\) be fixed, \(k\geq 1\), \(n \geq 1\), and let \(S\) be a simply connected orthogonal polygon in the plane. For \(T \subseteq S, T\) lies in a staircase \(n\)-convex orthogonal polygon \(P\) in \(S\) if and only if every two points of \(T\) see each other via staircase \(n\)-paths in \(S\). This leads to a characterization for those sets \(S\) expressible as a union of \(k\) staircase \(n\)-convex polygons \(P_i\), \(1 \leq i \leq k\).

MSC:

52A35 Helly-type theorems and geometric transversal theory

Keywords:

orthogonal polygons; staircase \(n\)-convex polygons
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\textit{M. Breen}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 50, No. 1, 23--28 (2011; Zbl 1244.52009)
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References:

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