The Number of Generalized Balanced Lines.
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| Title: | The Number of Generalized Balanced Lines. |
|---|---|
| Authors: | Orden, David1 david.orden@uah.es, Ramos, Pedro1 pedro.ramos@uah.es, Salazar, Gelasio2 gsalazar@dec1.ifisica.uaslp.mx |
| Source: | Discrete & Computational Geometry. Dec2010, Vol. 44 Issue 4, p805-811. 7p. |
| Subjects: | Number theory, Line geometry, Mathematical sequences, Set theory, Fixed point theory, Mathematical proofs, Triangles |
| Abstract: | Let S be a set of r red points and b= r+2 δ blue points in general position in the plane, with δ≥0. A line ℓ determined by them is balanced if in each open half-plane bounded by ℓ the difference between the number of blue points and red points is δ. We show that every set S as above has at least r balanced lines. The proof is a refinement of the ideas and techniques of Pach and Pinchasi (Discrete Comput. Geom. 25:611-628, ), where the result for δ=0 was proven, and introduces a new technique: sliding rotations. [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 |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 54326378 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The Number of Generalized Balanced Lines. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Orden%2C+David%22">Orden, David</searchLink><relatesTo>1</relatesTo><i> david.orden@uah.es</i><br /><searchLink fieldCode="AR" term="%22Ramos%2C+Pedro%22">Ramos, Pedro</searchLink><relatesTo>1</relatesTo><i> pedro.ramos@uah.es</i><br /><searchLink fieldCode="AR" term="%22Salazar%2C+Gelasio%22">Salazar, Gelasio</searchLink><relatesTo>2</relatesTo><i> gsalazar@dec1.ifisica.uaslp.mx</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+%26+Computational+Geometry%22">Discrete & Computational Geometry</searchLink>. Dec2010, Vol. 44 Issue 4, p805-811. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink><br /><searchLink fieldCode="DE" term="%22Line+geometry%22">Line geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+sequences%22">Mathematical sequences</searchLink><br /><searchLink fieldCode="DE" term="%22Set+theory%22">Set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Fixed+point+theory%22">Fixed point theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+proofs%22">Mathematical proofs</searchLink><br /><searchLink fieldCode="DE" term="%22Triangles%22">Triangles</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Let S be a set of r red points and b= r+2 δ blue points in general position in the plane, with δ≥0. A line ℓ determined by them is balanced if in each open half-plane bounded by ℓ the difference between the number of blue points and red points is δ. We show that every set S as above has at least r balanced lines. The proof is a refinement of the ideas and techniques of Pach and Pinchasi (Discrete Comput. Geom. 25:611-628, ), where the result for δ=0 was proven, and introduces a new technique: sliding rotations. [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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00454-010-9253-4 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 805 Subjects: – SubjectFull: Number theory Type: general – SubjectFull: Line geometry Type: general – SubjectFull: Mathematical sequences Type: general – SubjectFull: Set theory Type: general – SubjectFull: Fixed point theory Type: general – SubjectFull: Mathematical proofs Type: general – SubjectFull: Triangles Type: general Titles: – TitleFull: The Number of Generalized Balanced Lines. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Orden, David – PersonEntity: Name: NameFull: Ramos, Pedro – PersonEntity: Name: NameFull: Salazar, Gelasio IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2010 Type: published Y: 2010 Identifiers: – Type: issn-print Value: 01795376 Numbering: – Type: volume Value: 44 – Type: issue Value: 4 Titles: – TitleFull: Discrete & Computational Geometry Type: main |
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