Quanyu Tang

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20242026

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7 papers · 1 filter

math.CO2026

Global Product Intersection Sets in Semigroups

Wouter van Doorn, Pietro Monticone, Quanyu Tang

For a family $(A_{q})_{q \in Q}$ of subsets of a semigroup, the product intersection set records those exponents $h \in N$ for which the $h$ -fold product set of the intersect…

math.CO2026

On Spielman's Laplacian Eigenratio Conjecture and Related Problems

Jie Ma, Quanyu Tang, Yuchang Wang +1

Let $G$ be an $n$ -vertex graph with Laplacian eigenvalues $0 = λ_{1} (G) \leq λ_{2} (G) \leq \dots \leq λ_{n} (G)$ . Motivated by the Alon-Boppana bound and the Ramanujan phenomenon for regular grap…

math.CO2026

Optimal bounds for an Erdős problem on matching integers to distinct multiples

Wouter van Doorn, Yanyang Li, Quanyu Tang

Let $f (m)$ be the largest integer such that for every set $A = {a_{1} < \dots < a_{m}}$ of $m$ positive integers and every open interval $I$ of length $2 a_{m}$ , there exist at least $…

math.CO2026

An Erdős--Trotter problem on antichains with multiplicity $r$ on each occurring level

Yixin He, Quanyu Tang

Fix an integer $r \geq 2$ . For each $n$ we consider families $F \subseteq 2^{[n]}$ that form an antichain and have the property that, for every $t$ , if there exists $A\in\math…

math.CO2026

An Erdős problem on random subset sums in finite abelian groups

Jie Ma, Quanyu Tang

Let $f (N)$ denote the least integer $k$ such that, if $G$ is an abelian group of order $N$ and $A \subseteq G$ is a uniformly random $k$ -element subset, then with probability at le…

math.CO2026

On the maximum product of distances of diameter $2$ point sets

Stijn Cambie, Arne Decadt, Yanni Dong +2

We consider a problem posed by Erdős, Herzog and Piranian on the maximum product of distances of a point set of order $n$ with a given diameter. We prove that it is sufficient to c…

math.CO2026

Largest Sidon subsets in weak Sidon sets

Jie Ma, Quanyu Tang

A finite set $S \subset R$ is called a Sidon set if all sums $x + y$ with $x, y \in S$ and $x \leq y$ are distinct, and a weak Sidon set if all sums $x + y$ with $ x,y…

Global Product Intersection Sets in Semigroups

On Spielman's Laplacian Eigenratio Conjecture and Related Problems

Optimal bounds for an Erdős problem on matching integers to distinct multiples

An Erdős--Trotter problem on antichains with multiplicity r on each occurring level

An Erdős problem on random subset sums in finite abelian groups

On the maximum product of distances of diameter 2 point sets

Largest Sidon subsets in weak Sidon sets

An Erdős--Trotter problem on antichains with multiplicity $r$ on each occurring level

On the maximum product of distances of diameter $2$ point sets