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

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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### References:

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