Decreasing Paths of Polygons.
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| Title: | Decreasing Paths of Polygons. |
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| Authors: | Kulp, Isaac1 (AUTHOR) isaac_kulp1@baylor.edu, Ochanine, Charlotte2 (AUTHOR) charlotte.ochanine@louisiana.edu, Richard, Logan3 (AUTHOR) richalog@oregonstate.edu, Robert, Leonel2 (AUTHOR) lrobert@louisiana.edu, Whitman, Scott2 (AUTHOR) scott.whitman1@louisiana.edu |
| Source: | Discrete & Computational Geometry. Jul2026, Vol. 76 Issue 1, p121-176. 56p. |
| Subjects: | Polygons, Convex domains, Markov processes, Triangles |
| 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, these problems were investigated by Goodman, Johansen, Ramsey, and Frydman among others, in connection with the embeddability problem for non-homogeneous Markov processes. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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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, these problems were investigated by Goodman, Johansen, Ramsey, and Frydman among others, in connection with the embeddability problem for non-homogeneous Markov processes. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 01795376 |
| DOI: | 10.1007/s00454-025-00750-5 |
