REU Project - detail
- Venn diagrams and related structures
- Project Year: 2024
- REU Student (s): Adam Dzavoronok | Charles University (Prague, Czech Republic) | Tymofii Reizin | Charles University (Prague, Czech Republic) | Jakub Sosovicka | Charles University (Prague, Czech Republic)
- Student 1 Institution: Charles University (Prague, Czech Republic)
- Student 2 Institution: Charles University (Prague, Czech Republic)
- Project Mentor: Bhargav Narayanan
- Project Mentor Area: Mathematics
- Project Abstract:
A hypergraph ℋ on {1 ... n} is just a collection of subsets of {1 ... n}. We say that there is a "k-Venn diagram" in ℋ if there are k sets ( A1, ... , Ak ) in ℋ such that all 2k intersections ( B1 ∩ ... ∩ Bk ) are non-empty where each Bi can either be Ai or the complement of Ai (equivalently, if we draw the Venn diagram associated with (A1, ... , Ak), all the regions of this picture are nonempty). Our goal is to try to understand the following question: how many sets can our hypergraph ℋ have if it fails to contain a k-Venn diagram?