Decreasing Paths of Polygons.
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| Title: | Decreasing Paths of Polygons. |
|---|---|
| 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] |
| Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 194776504 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Decreasing Paths of Polygons. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kulp%2C+Isaac%22">Kulp, Isaac</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> isaac_kulp1@baylor.edu</i><br /><searchLink fieldCode="AR" term="%22Ochanine%2C+Charlotte%22">Ochanine, Charlotte</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> charlotte.ochanine@louisiana.edu</i><br /><searchLink fieldCode="AR" term="%22Richard%2C+Logan%22">Richard, Logan</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> richalog@oregonstate.edu</i><br /><searchLink fieldCode="AR" term="%22Robert%2C+Leonel%22">Robert, Leonel</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> lrobert@louisiana.edu</i><br /><searchLink fieldCode="AR" term="%22Whitman%2C+Scott%22">Whitman, Scott</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> scott.whitman1@louisiana.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+%26+Computational+Geometry%22">Discrete & Computational Geometry</searchLink>. Jul2026, Vol. 76 Issue 1, p121-176. 56p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Polygons%22">Polygons</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+domains%22">Convex domains</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink><br /><searchLink fieldCode="DE" term="%22Triangles%22">Triangles</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=194776504 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00454-025-00750-5 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 56 StartPage: 121 Subjects: – SubjectFull: Polygons Type: general – SubjectFull: Convex domains Type: general – SubjectFull: Markov processes Type: general – SubjectFull: Triangles Type: general Titles: – TitleFull: Decreasing Paths of Polygons. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kulp, Isaac – PersonEntity: Name: NameFull: Ochanine, Charlotte – PersonEntity: Name: NameFull: Richard, Logan – PersonEntity: Name: NameFull: Robert, Leonel – PersonEntity: Name: NameFull: Whitman, Scott IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 01795376 Numbering: – Type: volume Value: 76 – Type: issue Value: 1 Titles: – TitleFull: Discrete & Computational Geometry Type: main |
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