Caps and Wickets
Abstract
Let $H_n^{(3)}$ be a 3-uniform linear hypergraph, i.e. any two edges have at most one vertex common. A special hypergraph, {\em wicket}, is formed by three rows and two columns of a $3 \times 3$ point matrix. In this note, we give a new lower bound on the Turán number of wickets using estimates on cap sets. We also show that this problem is closely connected to important questions in additive combinatorics.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.00923
- arXiv:
- arXiv:2405.00923
- Bibcode:
- 2024arXiv240500923F
- Keywords:
-
- Mathematics - Combinatorics
- E-Print:
- An updated version, correcting a gap in the previous version