Quanyu Tang

collaborators

16 papers

math.NT2026

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.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 $0 = I^»_{1} (G) \leq I^»_{2} (G) \leq \dots \leq I^»_{n} (G)$ . Motivated by the Alon-Boppana bound and the Ramanujan phenomenon for regular g…

math.NT2026

A counterexample to a conjecture of SÃ¡rkÃ¶zy on sums and products modulo a prime

Quanyu Tang

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

math.CO2026

Optimal bounds for an ErdÅs 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 ErdÅs--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…

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

Global Product Intersection Sets in Semigroups

On Spielman's Laplacian Eigenratio Conjecture and Related Problems

A counterexample to a conjecture of SÃ¡rkÃ¶zy on sums and products modulo a prime

Optimal bounds for an ErdÅs problem on matching integers to distinct multiples

An ErdÅs--Trotter problem on antichains with multiplicity r on each occurring level

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

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

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