Quanyu Tang

activity

20242026

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4 papers · 1 filter

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=…

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

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