Xiaoyu He

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5 papers · 1 filter

math.CO2026

Hypergraph Ramsey numbers with quasipolynomial growth rate

Xiaoyu He, Jiaxi Nie, Logan Post +1

For a 3-uniform hypergraph (3-graph) $F$ , let $r (F, n)$ be the smallest $N$ such that any $N$ -vertex $F$ -free 3-graph has an independent set of size $n$ . We construct a $3$ -graph $H…

math.CO2024

When are off-diagonal hypergraph Ramsey numbers polynomial?

David Conlon, Jacob Fox, Benjamin Gunby +5

A natural open problem in Ramsey theory is to determine those $3$ -graphs $H$ for which the off-diagonal Ramsey number $r (H, K_{n}^{(3)})$ grows polynomially with $n$ . We make substan…

math.CO2024

Big line or big convex polygon

David Conlon, Jacob Fox, Xiaoyu He +3

Let $E S_{ℓ} (n)$ be the minimum $N$ such that every $N$ -element point set in the plane contains either $ℓ$ collinear members or $n$ points in convex position. We prove that th…

math.CO2024

On off-diagonal hypergraph Ramsey numbers

David Conlon, Jacob Fox, Benjamin Gunby +4

A fundamental problem in Ramsey theory is to determine the growth rate in terms of $n$ of the Ramsey number $r (H, K_{n}^{(3)})$ of a fixed $3$ -uniform hypergraph $H$ versus the compl…

math.CO2024

A question of Erdős and Graham on Egyptian fractions

David Conlon, Jacob Fox, Xiaoyu He +4

Answering a question of Erdős and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive inte…