## Staircase $$k$$-kernels for orthogonal polygons.(English)Zbl 0742.52006

Let $$S\neq\emptyset$$ be a finite union of boxes in $$\mathbb{R}^ 2$$ whose edges are parallel to the coordinate axes. If $$S$$ is simply connected and starshaped via staircase paths, then the staircase kernel of $$S$$, $$\hbox{Ker} S$$, as the intersection of all maximal orthogonally convex polygons in $$S$$, and $$\hbox{Ker} S$$ is an orthogonally convex region. In general, when $$S$$ is starshaped via staircase paths, then each component of $$\hbox{Ker} S$$ is an orthogonally convex polygon. However, there may be maximal orthogonally convex polygons in $$S$$ which fail to contain $$\hbox{Ker} S$$.
Reviewer: M.Breen

### MSC:

 52A30 Variants of convex sets (star-shaped, ($$m, n$$)-convex, etc.)
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### References:

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