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- W4386043863 abstract "Unlike graphs, determining Tur'{a}n densities of hypergraphs is known to be notoriously hard in general. The essential reason is that for many classical families of $r$-uniform hypergraphs $mathcal{F}$, there are perhaps many near-extremal $mathcal{M}_t$-free configurations with very different structure. Such a phenomenon is called not stable, and Liu and Mubayi gave a first not stable example. Another perhaps reason is that little is known about the set consisting of all possible Tur'{a}n densities which has cardinality of the continuum. Let $tge 2$ be an integer. In this paper, we construct a finite family $mathcal{M}_t$ of 3-uniform hypergraphs such that the Tur'{a}n density of $mathcal{M}_t$ is irrational, and there are $t$ near-extremal $mathcal{M}_t$-free configurations that are far from each other in edit-distance. This is the first not stable example that has an irrational Tur'{a}n density. It also provides a new phenomenon about feasible region functions." @default.
- W4386043863 created "2023-08-22" @default.
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- W4386043863 date "2023-08-18" @default.
- W4386043863 modified "2023-10-16" @default.
- W4386043863 title "Hypergraphs with irrational Tur'{a}n density and many extremal configurations" @default.
- W4386043863 doi "https://doi.org/10.48550/arxiv.2308.09382" @default.
- W4386043863 hasPublicationYear "2023" @default.
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