Geodesic
Hypergraphs with infinitely many extremal constructions
Discrete analysis (2023) Cet article a éte moissonné depuis la source Scholastica

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We give the first exact and stability results for a hypergraph Turán problem with infinitely many extremal constructions that are far from each other in edit-distance. This includes an example of triple systems with Turán 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.
Publié le : 
@article{DAS_2023_a4,
     author = {Jianfeng Hou and Heng Li and Xizhi Liu and Dhruv Mubayi and Yixiao Zhang},
     title = {Hypergraphs with infinitely many extremal constructions},
     journal = {Discrete analysis},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2023_a4/}
}
TY  - JOUR
AU  - Jianfeng Hou
AU  - Heng Li
AU  - Xizhi Liu
AU  - Dhruv Mubayi
AU  - Yixiao Zhang
TI  - Hypergraphs with infinitely many extremal constructions
JO  - Discrete analysis
PY  - 2023
UR  - http://geodesic.mathdoc.fr/item/DAS_2023_a4/
LA  - en
ID  - DAS_2023_a4
ER  - 
%0 Journal Article
%A Jianfeng Hou
%A Heng Li
%A Xizhi Liu
%A Dhruv Mubayi
%A Yixiao Zhang
%T Hypergraphs with infinitely many extremal constructions
%J Discrete analysis
%D 2023
%U http://geodesic.mathdoc.fr/item/DAS_2023_a4/
%G en
%F DAS_2023_a4
Jianfeng Hou; Heng Li; Xizhi Liu; Dhruv Mubayi; Yixiao Zhang. Hypergraphs with infinitely many extremal constructions. Discrete analysis (2023). http://geodesic.mathdoc.fr/item/DAS_2023_a4/