Shumin Sun

collaborators

7 papers

math.CO2026

The quadratic Brown--Erdős--Sós problem for 3-uniform hypergraphs with 8 and 9 edges

Levente Bodnár, Oleg Pikhurko, Shumin Sun +2

The famous and actively studied problem of Brown--Erdős--Sós from 1973 asks for $f^{(r)} (n; s, k)$ , the maximum number of edges in an $r$ -graph with $n$ vertices in which no $s$ vert…

math.CO2026

The inducibility of 6-vertex graphs

Levente Bodnár, Jun Gao, Jared León +3

The inducibility constant $λ_{F}$ of a graph $F$ is the asymptotically maximum induced density of $F$ in a growing sequence of graphs. This paper systematically investigates the ca…

math.CO2026

Strong non-principality of positive codegree Turán density

Levente Bodnár, Jun Gao, Oleg Pikhurko +2

The \emph{minimum positive codegree} $δ_{k - 1}^{+} (G)$ 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 s…

math.CO2026

Rational codegree Turán 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 $δ_{k - 1} (H)$ is the largest integer $t$ such that every $(k - 1)$ -subset of $V (H)$ is contained in at lea…

math.CO2025

Covering large-dimensional Euclidean spaces by random translates of a given convex body

Boris Bukh, Jun Gao, Xizhi Liu +2

Determining the minimum density of a covering of $R^{n}$ by Euclidean unit balls as $n \to \infty$ is a major open problem, with the best known results being the lower bound…

math.MG2025

New upper bound for lattice covering by spheres

Jun Gao, Xizhi Liu, Oleg Pikhurko +1

We show that there exists a lattice covering of $R^{n}$ by Eucledian spheres of equal radius with density $O (n ln^{β} n)$ as $n \to \infty$ , where \begin{align*} β:= \…

math.CO2025

On the quadratic 8-edge case of the Brown-Erdős-Sós problem

Oleg Pikhurko, Shumin Sun

Let $f^{(r)} (n; s, k)$ be the maximum number of edges in an $n$ -vertex $r$ -uniform hypergraph containing no $k$ edges on at most $s$ vertices. Brown, Erdős and Sós conjectured in 197…