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The uniform Tur\'an density of large stars
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abstract
We asymptotically resolve the the uniform Tur\'an density problem for the large stars. In particular, we show that the uniform Tur\'an density of the $k$-star $S_k$ is $\frac{k^2-5k+7}{(k-1)^2}$ for $k\ge 48$, matching a lower construction by Reiher, R\"odl and Schacht.
Forward citations
Cited by 4 Pith papers
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On possible uniform Tur\'an densities
The set of uniform Turan densities of finite families contains every palette Lagrangian, and therefore contains irrational numbers.
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Finite palette endpoints and degree-square Tur\'an problems
Proves exact degree-square Turán formulas for tournament palettes via auxiliary digraphs and majorization, yielding finite 3-graphs with uniform densities approaching 1/3.
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Uniform Tur\'an density beyond 3-graphs
For every r≥3 there exist r-uniform hypergraphs whose uniform Turán density is 1/4, and others whose uniform Turán density is binom(r,2)^{-binom(r,2)}; the r≥5 cases are the first explicit non-zero values.
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Uniform Tur\'an density -- palette classification
A hypergraph exists that is colorable by each of given palettes but not by an additional palette exactly when no palette homomorphism exists to that additional palette or its inverse.
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