New results of Bollobás-type theorem for affine subspaces and projective subspaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913653084651520 |
|---|---|
| author | Yu, Shuhui Wang, Xin |
| author_facet | Yu, Shuhui Wang, Xin |
| contents | Bollobás-type theorem has received a lot of attention due to its application in graph theory. In 2015, Gábor Heged{ü}s gave an upper bound of bollobás-type affine subspace families for $q\neq 2$, and constructed an almost sharp affine subspaces pair families. In this note, we prove a new upper bound for bollobás-type affine subspaces without the requirement of $q\neq 2$, and construct a pair of families of affine subspaces, which shows that our upper bound is sharp. We also give an upper bound for bollobás-type projective subspaces, and prove that the Heged{ü}s's conjecture holds when $q=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New results of Bollobás-type theorem for affine subspaces and projective subspaces Yu, Shuhui Wang, Xin Combinatorics Bollobás-type theorem has received a lot of attention due to its application in graph theory. In 2015, Gábor Heged{ü}s gave an upper bound of bollobás-type affine subspace families for $q\neq 2$, and constructed an almost sharp affine subspaces pair families. In this note, we prove a new upper bound for bollobás-type affine subspaces without the requirement of $q\neq 2$, and construct a pair of families of affine subspaces, which shows that our upper bound is sharp. We also give an upper bound for bollobás-type projective subspaces, and prove that the Heged{ü}s's conjecture holds when $q=2$. |
| title | New results of Bollobás-type theorem for affine subspaces and projective subspaces |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2501.09215 |