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Hypergraphs with infinitely many extremal constructions
- Publication Year :
- 2022
-
Abstract
- We give the first exact and stability results for a hypergraph Tur\'{a}n problem with infinitely many extremal constructions that are far from each other in edit-distance. This includes an example of triple systems with Tur\'{a}n density $2/9$, thus answering some questions posed by the third and fourth authors and Reiher about the feasible region of hypergraphs. Our results also provide extremal constructions whose shadow density is a transcendental number. Our novel approach is to construct certain multilinear polynomials that attain their maximum (in the standard simplex) on a line segment and then to use these polynomials to define an operation on hypergraphs that gives extremal constructions.<br />Comment: journal version, Discrete Analysis 2023:18, 34 pp
- Subjects :
- Mathematics - Combinatorics
05C65, 05C35, 05D99
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2206.03948
- Document Type :
- Working Paper