An algebraic approach to Erdős-Ko-Rado sets of flags in spherical buildings II
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916350971084800 |
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| author | De Beule, Jan Mattheus, Sam Metsch, Klaus |
| author_facet | De Beule, Jan Mattheus, Sam Metsch, Klaus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An algebraic approach to Erdős-Ko-Rado sets of flags in spherical buildings II De Beule, Jan Mattheus, Sam Metsch, Klaus Combinatorics 05E18, 05C50, 05E30 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. |
| title | An algebraic approach to Erdős-Ko-Rado sets of flags in spherical buildings II |
| topic | Combinatorics 05E18, 05C50, 05E30 |
| url | https://arxiv.org/abs/2408.05015 |