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• Intervals of hypergraph Tur\'an densities math.CO · 2026-05-25 · unverdicted · none · ref 24

  The set of Turán densities of (possibly infinite) families of r-graphs contains non-degenerate intervals for every r≥3.

• Uniform Tur\'an densities of $k$-uniform hypergraphs math.CO · 2026-05-14 · unverdicted · none · ref 18

  A new palette framework reduces (k-2)-uniform Turán densities of k-graphs to palette-homomorphism problems and yields exact values including (r-1)/r, (r-1)^2/r^2, and (k-1)^k/k^k for various k and r.

• Finite palette endpoints and degree-square Tur\'an problems math.CO · 2026-06-02 · accept · none · ref 9

  Finite palette avoidance for self-converse tournaments reduces exactly to a one-sided degree-square Turán problem, and for the directed triangle this gives sharp endpoints whose 3-graph uniform Turán densities accumulate at 1/3.

• A single $3$-graph with infinite stability number math.CO · 2026-05-21 · unverdicted · none · ref 17

  Explicit construction of a single 3-graph with infinite stability number, extending the phenomenon from finite forbidden families to the single-forbidden case.

• Tur\'an density of stars in uniformly dense hypergraphs math.CO · 2025-10-14 · conditional · none · ref 8

  The paper shows π₁(S_k) equals (k²-5k+7)/(k-1)² for k≥9 by improving the optimality range of the palette construction.