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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.09215 |
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Table of 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 $q=2$.