An algebraic approach to Erdős-Ko-Rado sets of flags in spherical buildings II.
Saved in:
| Title: | An algebraic approach to Erdős-Ko-Rado sets of flags in spherical buildings II. |
|---|---|
| Authors: | De Beule, Jan1 (AUTHOR) jan.de.beule@vub.be, Mattheus, Sam1 (AUTHOR) sam.mattheus@vub.be, Metsch, Klaus2 (AUTHOR) klaus.metsch@math.uni-giessen.de |
| Source: | Linear Algebra & its Applications. May2026, Vol. 737, p227-262. 36p. |
| Subjects: | Algebraic combinatorics, Combinatorics, Graph theory, Invariant subspaces, Algebra |
| Abstract: | We continue our investigation of Erdős-Ko-Rado (EKR) sets of flags in spherical buildings. In previous work, we used the theory of buildings and Iwahori-Hecke algebras to obtain upper bounds on their size. As the next step towards the classification of the maximal EKR-sets, we describe the eigenspaces for the smallest eigenvalue of the opposition graphs. We determine their multiplicity and provide a combinatorial description of spanning sets of these subspaces, from which a complete description of the maximal Erdős-Ko-Rado sets of flags may potentially be found. This was recently shown to be possible for type A n , n odd, by Heering, Lansdown, and the last author by making use of the current work. [ABSTRACT FROM AUTHOR] |
| Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. 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: 192196637 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: An algebraic approach to Erdős-Ko-Rado sets of flags in spherical buildings II. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22De+Beule%2C+Jan%22">De Beule, Jan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jan.de.beule@vub.be</i><br /><searchLink fieldCode="AR" term="%22Mattheus%2C+Sam%22">Mattheus, Sam</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sam.mattheus@vub.be</i><br /><searchLink fieldCode="AR" term="%22Metsch%2C+Klaus%22">Metsch, Klaus</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> klaus.metsch@math.uni-giessen.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. May2026, Vol. 737, p227-262. 36p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Algebraic+combinatorics%22">Algebraic combinatorics</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorics%22">Combinatorics</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Invariant+subspaces%22">Invariant subspaces</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We continue our investigation of Erdős-Ko-Rado (EKR) sets of flags in spherical buildings. In previous work, we used the theory of buildings and Iwahori-Hecke algebras to obtain upper bounds on their size. As the next step towards the classification of the maximal EKR-sets, we describe the eigenspaces for the smallest eigenvalue of the opposition graphs. We determine their multiplicity and provide a combinatorial description of spanning sets of these subspaces, from which a complete description of the maximal Erdős-Ko-Rado sets of flags may potentially be found. This was recently shown to be possible for type A n , n odd, by Heering, Lansdown, and the last author by making use of the current work. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. 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=192196637 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.laa.2026.02.021 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 36 StartPage: 227 Subjects: – SubjectFull: Algebraic combinatorics Type: general – SubjectFull: Combinatorics Type: general – SubjectFull: Graph theory Type: general – SubjectFull: Invariant subspaces Type: general – SubjectFull: Algebra Type: general Titles: – TitleFull: An algebraic approach to Erdős-Ko-Rado sets of flags in spherical buildings II. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: De Beule, Jan – PersonEntity: Name: NameFull: Mattheus, Sam – PersonEntity: Name: NameFull: Metsch, Klaus IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00243795 Numbering: – Type: volume Value: 737 Titles: – TitleFull: Linear Algebra & its Applications Type: main |
| ResultId | 1 |
