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Hypergraphs accumulate infinitely often

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arxiv 2506.03080 v1 pith:BK557VPB submitted 2025-06-03 math.CO

Hypergraphs accumulate infinitely often

David Conlon , Bjarne Sch\"ulke This is my paper
classification math.CO
keywords accumulationhypergraphsinfinitelyaccumulatedensitiesearliereveryextends
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We show that the set $\Pi^{(k)}$ of Tur\'an densities of $k$-uniform hypergraphs has infinitely many accumulation points in $[0,1)$ for every $k \geq 3$. This extends an earlier result of ours showing that $\Pi^{(k)}$ has at least one such accumulation point.

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  1. Tree suspensions and transfer functions for single degree Tur\'an spectra

    math.CO 2026-07 accept novelty 7.5

    Tree suspensions realize three transfer functions on single degree Turán spectra, yielding infinitely many accumulation points for all parameters and arbitrarily high algebraic degree for ordinary and half-or-higher d...