Mingyuan Rong

activity

20242026

collaborators

6 papers

math.CO2026

Strong non-principality of positive codegree TurÃ¡n density

Levente BodnÃ¡r, Jun Gao, Oleg Pikhurko +2

The \emph{minimum positive codegree} $I^´_{k - 1}^{+} (G)$ of a $k$ -graph $G$ is the minimum, over all $(k - 1)$ -sets that lie in at least one edge, of the number of edges containing that…

math.CO2026

Rational codegree TurÃ¡n density of hypergraphs

Jun Gao, Oleg Pikhurko, Mingyuan Rong +1

Let $H$ be a $k$ -graph (i.e. a $k$ -uniform hypergraph). Its minimum codegree $I^´_{k - 1} (H)$ is the largest integer $t$ such that every $(k - 1)$ -subset of $V (H)$ is contained in at le…

math.CO2025

The codegree TurÃ¡n density of tight cycles

Jie Ma, Mingyuan Rong

The codegree TurÃ¡n density $I^^{3} (F)$ of a $k$ -uniform hypergraph $F$ is the minimum real number $I^^{3} \geq 0$ such that every $k$ -uniform hypergraph on sufficiently many $n$ vertices, i…

math.CO2025

Recent advances in arrow relations and traces of sets

Mingze Li, Jie Ma, Mingyuan Rong

The arrow relation, a central concept in extremal set theory, captures quantitative relationships between families of sets and their traces. Formally, the arrow relation $(n, m) \r…

math.CO2025

Variants of VC dimension and their applications to dynamics

Guorong Gao, Jie Ma, Mingyuan Rong +1

Since its introduction by Vapnik and Chervonenkis in the 1960s, the VC dimension and its variants have played a central role in numerous fields. In this paper, we investigate sever…

math.CO2024

Exact results on traces of sets

Mingze Li, Jie Ma, Mingyuan Rong

For non-negative integers $n$ , $m$ , $a$ and $b$ , we write $(n, m) \to (a, b)$ if for every family $F \subseteq 2^{[n]}$ with $|\mathcal{F}|…