View in EDS

Extension-Lifting Bijections for Oriented Matroids.

Saved in:
Bibliographic Details
Title: Extension-Lifting Bijections for Oriented Matroids.
Authors: Backman, Spencer1 (AUTHOR) spencer.backman@uvm.edu, Santos, Francisco2 (AUTHOR) francisco.santos@unican.es, Yuen, Chi Ho3 (AUTHOR) chyuen@math.nctu.edu.tw
Source: Discrete & Computational Geometry. Apr2026, Vol. 75 Issue 3, p969-994. 26p.
Subjects: Matroids, Mathematical mappings
Abstract: Extending the notion of geometric bijections for regular matroids, introduced by the first and third author with Matthew Baker, we describe a family of bijections between bases of an oriented matroid and special reorientations of it. These bijections are specified by a pair of circuit and cocircuit signatures coming respectively from a generic single-element lifting and extension. We then characterize generic single-element liftings and extensions using these bijections. We also explain the relation of our work with works of Gioan–Las Vergnas and Ding. Some implications in oriented matroid programming and oriented matroid triangulations are also discussed. [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 Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 192769855
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Extension-Lifting Bijections for Oriented Matroids.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Backman%2C+Spencer%22">Backman, Spencer</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> spencer.backman@uvm.edu</i><br /><searchLink fieldCode="AR" term="%22Santos%2C+Francisco%22">Santos, Francisco</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> francisco.santos@unican.es</i><br /><searchLink fieldCode="AR" term="%22Yuen%2C+Chi+Ho%22">Yuen, Chi Ho</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> chyuen@math.nctu.edu.tw</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Discrete+%26+Computational+Geometry%22">Discrete & Computational Geometry</searchLink>. Apr2026, Vol. 75 Issue 3, p969-994. 26p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Matroids%22">Matroids</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+mappings%22">Mathematical mappings</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Extending the notion of geometric bijections for regular matroids, introduced by the first and third author with Matthew Baker, we describe a family of bijections between bases of an oriented matroid and special reorientations of it. These bijections are specified by a pair of circuit and cocircuit signatures coming respectively from a generic single-element lifting and extension. We then characterize generic single-element liftings and extensions using these bijections. We also explain the relation of our work with works of Gioan–Las Vergnas and Ding. Some implications in oriented matroid programming and oriented matroid triangulations are also discussed. [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=192769855
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s00454-026-00834-w
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 26
        StartPage: 969
    Subjects:
      – SubjectFull: Matroids
        Type: general
      – SubjectFull: Mathematical mappings
        Type: general
    Titles:
      – TitleFull: Extension-Lifting Bijections for Oriented Matroids.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Backman, Spencer
      – PersonEntity:
          Name:
            NameFull: Santos, Francisco
      – PersonEntity:
          Name:
            NameFull: Yuen, Chi Ho
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 04
              Text: Apr2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 01795376
          Numbering:
            – Type: volume
              Value: 75
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: Discrete & Computational Geometry
              Type: main
ResultId 1