Ruben Ascoli

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math.CO2026

A reformulation of the discrete Convexity Conjecture via $k$ -thresholds

Ruben Ascoli, Xiaoyu He, Jinyoung Park +1

We introduce the notion of " $k$ -thresholds'' and show that Talagrand's discrete convexity conjecture is equivalent to the assertion that, for some universal integer $k \geq 2$ , the…

math.CO2025

Polynomial-to-exponential transition in 3-uniform Ramsey numbers

Ruben Ascoli, Xiaoyu He, Hung-Hsun Hans Yu

Let $r_{k} (s, e; t)$ denote the smallest $N$ such that any red/blue edge coloring of the complete $k$ -uniform hypergraph on $N$ vertices contains either $e$ red edges among some $s$ …

math.CO2025

Rational values of the weak saturation limit

Ruben Ascoli, Xiaoyu He

Given a graph $F$ , a graph $G$ is weakly $F$ -saturated if all non-edges of $G$ can be added in some order so that each new edge introduces a copy of $F$ . The weak saturation number…

A reformulation of the discrete Convexity Conjecture via k-thresholds

Polynomial-to-exponential transition in 3-uniform Ramsey numbers

Rational values of the weak saturation limit

A reformulation of the discrete Convexity Conjecture via $k$ -thresholds