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arXiv · 2207.06290

Planar convex codes are decidable

Boris Bukh·R. Amzi Jeffs
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Abstract

We show that every convex code realizable by compact sets in the plane admits a realization consisting of polygons, and analogously every open convex code in the plane can be realized by interiors of polygons. We give factorial-type bounds on the number of vertices needed to form such realizations. Consequently we show that there is an algorithm to decide whether a convex code admits a closed or open realization in the plane.

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Boris Bukh, R. Amzi Jeffs. 2022-12-13. Planar convex codes are decidable. https://arxiv.org/abs/2207.06290

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