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arXiv · 2402.12643

Decreasing paths of polygons

Isaac Kulp·Charlotte Ochanine·Logan Richard·Leonel Robert·Scott Whitman
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Abstract

We call a continuous path of polygons decreasing if the convex hulls of the polygons form a decreasing family of sets. For an arbitrary polygon of more than three vertices, we characterize the polygons contained in it that can be reached by a decreasing path (attainability problem), and we show that this can be done by a finite application of "pull-in" moves (bang-bang problem). In the case of triangles, this problems was investigated by Goodman, Johansen, Ramsey, and Frydman among others, in connection with the embeddability problem for non-homogeneous Markov processes.

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Isaac Kulp, Charlotte Ochanine, Logan Richard, Leonel Robert, Scott Whitman. 2024-02-20. Decreasing paths of polygons. https://arxiv.org/abs/2402.12643

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