Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.09769 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918381553188864 |
|---|---|
| author | Heering, Philipp |
| author_facet | Heering, Philipp |
| contents | In the finite projective space PG$(2n,q)$ we consider flags of type $(n-1,n)$, that is, pairs $(A,B)$ consisting of an $(n-1)$-space $A$ and an $n$-space $B$ that are incident. Two such flags $(A_1,B_1)$ and $(A_2,B_2)$ are opposite if $A_1\cap B_2=A_2\cap B_1=\emptyset$. Let $Γ_{2n}$ be the graph whose vertices are the flags of type $(n-1,n)$ of PG$(2n,q)$, with two vertices being adjacent if the corresponding flags are opposite. Using the Erdős-Matching theorem for vector spaces shown by Ihringer, we determine, for $q$ large enough, the largest cocliques of $Γ_{2n}$ and obtain a stability result. This EKR-type theorem proves a conjecture of D'haeseleer, Metsch and Werner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09769 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cocliques in the Kneser graph on $(n-1,n)$-flags of PG$(2n,q)$ Heering, Philipp Combinatorics In the finite projective space PG$(2n,q)$ we consider flags of type $(n-1,n)$, that is, pairs $(A,B)$ consisting of an $(n-1)$-space $A$ and an $n$-space $B$ that are incident. Two such flags $(A_1,B_1)$ and $(A_2,B_2)$ are opposite if $A_1\cap B_2=A_2\cap B_1=\emptyset$. Let $Γ_{2n}$ be the graph whose vertices are the flags of type $(n-1,n)$ of PG$(2n,q)$, with two vertices being adjacent if the corresponding flags are opposite. Using the Erdős-Matching theorem for vector spaces shown by Ihringer, we determine, for $q$ large enough, the largest cocliques of $Γ_{2n}$ and obtain a stability result. This EKR-type theorem proves a conjecture of D'haeseleer, Metsch and Werner. |
| title | Cocliques in the Kneser graph on $(n-1,n)$-flags of PG$(2n,q)$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.09769 |