Quanyu Tang

activity

20242026

collaborators

16 papers

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.NT2026

A counterexample to a conjecture of Sárközy on sums and products modulo a prime

Quanyu Tang

Let $p$ be a prime and, for $A \subseteq F_{p}$ , define $A^{*} = (A + A) \cup (AA)$ . Sárközy conjectured that there exist constants $c > 0$ and $p_{0}$ such that, for every prime $p>p_…

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.CV2026

On Fuchs's additive intersection problem for the hyperbolic metric

Yixin He, Quanyu Tang

For hyperbolic domains $D_{1}, D_{2} \subset {z \in C : ∣ z ∣ < R}$ and $z \in D_{1} \cap D_{2}$ , we consider the ratio $\frac{λ _{D_{1} \cap D_{2}} ( z )}{λ _{D_{1}} ( z ) + λ _{D_{2}} ( z )} .$ We solve a pr…

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…

math.CV2026

Generalizing the Clunie--Hayman construction in an Erdős maximum-term problem

Yixin He, Quanyu Tang

Let $f (z) = \sum_{n \geq 0} a_{n} z^{n}$ be a transcendental entire function and write $M (r, f) := max_{∣ z ∣ = r} ∣ f (z) ∣$ and $μ (r, f) := max_{n \geq 0} ∣ a_{n} ∣ r^{n}$ . A problem of Erdős asks for the valu…

math.NT2026

Average first-passage times for character sums

Quanyu Tang, Hao Zhang

Let $ε > 0$ and, for an odd prime $p$ , set $S_{ℓ} (p) := n \leq ℓ \sum (\frac{n}{p}) .$ Define the first-passage time $$ f_\varepsilon(p):=\min\{\ell\ge 1:\ S…

math.NT2025

Harmonic LCM patterns and sunflower-free capacity

Quanyu Tang, Shengtong Zhang

Fix an integer $k \geq 3$ . Call a set $A \subseteq [N]$ LCM- $k$ -free if it does not contain distinct $a_{1}, \dots, a_{k}$ such that $lcm (a_{i}, a_{j})$ is the same for all $1\le i<j\le…

math.NT2025

The smallest denominator not contained in a unit fraction decomposition of $1$ with fixed length

Wouter van Doorn, Quanyu Tang

Let $v (k)$ be the smallest integer larger than $1$ that does not occur among the denominators in any identity of the form $1 = \frac{1}{n _{1}} + \dots + \frac{1}{n _{k}},$ where $1 \le n_1<\…

math.NT2025

An improved lower bound for Erdős--Szekeres products

Quanyu Tang

In 1959, Erdős and Szekeres posed a series of problems concerning the size of polynomials of the form $P_{n} (z) = j = 1 \prod n (1 - z^{s_{j}}),$ where $s_{1}, \dots, s_{n}$ are positi…

math.NT2025

On a conjecture of Erdős and Graham about the Sylvester's sequence

Zheng Li, Quanyu Tang

Let ${u_{n}}_{n = 1}^{\infty}$ be the Sylvester's sequence (sequence A000058 in the OEIS), and let $a_{1} < a_{2} < \dots$ be any other positive integer sequence satisfying $ \sum_{i=…

math.GM2024

A Note on a Recent Attempt to Prove the Irrationality of $ζ (5)$

Keyu Chen, Wei He, Yixin He +7

Recently Shekhar Suman [arXiv: 2407.07121v6 [math.GM] 3 Aug 2024] made an attempt to prove the irrationality of $ζ (5)$ . But unfortunately the proof is not correct. In this note, we…

Global Product Intersection Sets in Semigroups

On Spielman's Laplacian Eigenratio Conjecture and Related Problems

A counterexample to a conjecture of Sárközy on sums and products modulo a prime

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 Fuchs's additive intersection problem for the hyperbolic metric

On the maximum product of distances of diameter 2 point sets

Largest Sidon subsets in weak Sidon sets

Generalizing the Clunie--Hayman construction in an Erdős maximum-term problem

Average first-passage times for character sums

Harmonic LCM patterns and sunflower-free capacity

The smallest denominator not contained in a unit fraction decomposition of 1 with fixed length

An improved lower bound for Erdős--Szekeres products

On a conjecture of Erdős and Graham about the Sylvester's sequence

A Note on a Recent Attempt to Prove the Irrationality of ζ(5)

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

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

The smallest denominator not contained in a unit fraction decomposition of $1$ with fixed length

A Note on a Recent Attempt to Prove the Irrationality of $ζ (5)$