Eric Li

collaborators

13 papers

math.CO2026

The Godsil--McKay Asymptotic for Latin Rectangles in the Sublinear Range of Erdős Problem 725

Eric Li

Erdős Problem 725 asks for an asymptotic formula for the number $L_{k, n}$ of ordered, labelled $k \times n$ Latin rectangles. Godsil and McKay proved that $L_{k,n}\sim (n!)^k((n)_k/…

math.CO2026

A Resolution of Erdős Problem 550 on Tree versus Complete Multipartite Ramsey Numbers

Eric Li

We resolve Erdős Problem 550, originally asked as question (2) of Erdős, Faudree, Rousseau, and Schelp. Precisely, for fixed integers $k \geq 2$ and $1 \leq m_{1} \leq \dots \leq m_{k}$ ,…

math.NT2026

A Resolution of Erdős Problem 731 under Dyadic Regularity

Eric Li

We resolve Erdős Problem 731 under the explicit dyadic-regularity formalization of "reasonable." Let $A (n)$ be the least positive integer not dividing $(n 2 n)$ . On dyadic in…

math.CO2026

A Resolution of Erdős Problems 593 and 1177: Obligatory Triple Systems and Exact Spectra

Eric Li

We resolve Erdős Problems #593 and #1177. Problem #593 asks which finite triple systems occur in every uncountably chromatic triple system; the answer is exactly the class generate…

math.NT2026

A Resolution of Erdős Problem 768: the Sylow Divisor Condition

Eric Li

We resolve Erdős Problem 768. Let $A (x)$ count the positive integers $n \leq x$ such that, for every prime $p ∣ n$ , there is a divisor $d > 1$ of $n$ with $d \equiv 1 (mod p)$ . Erdős…

math.NT2026

A resolution of Erdős Problem 1061 on the sum-of-divisors function

Eric Li

We resolve Erdős Problem 1061, the question whether the number \[ S(x)=\#\{(a,b)\in\mathbb{N}^2:a+b\le x, \ σ(a)+σ(b)=σ(a+b)\} \] of ordered solutions has a linear asymptotic $S(x)…

math.NT2026

Prime-Power Rarefaction and a Density-One Lower Bound for Erdős Problem 400

Eric Li

For fixed $k \geq 2$ , let $g_{k} (n)$ be the greatest excess $a_{1} + \dots + a_{k} - n$ among positive integers $a_{i}$ satisfying $a_{1}! \dots a_{k}! ∣ n!$ . We prove that, for every $\varepsilon>…

math.NT2026

Square-Annular Dynamics and Coalescence Frontiers for $n + τ (n)$

Eric Li

Let $T (n) = n + τ (n)$ , where $τ$ is the divisor function. We study the Erdos-Graham coalescence problem by encoding finite-level obstructions in the divisor-successor graph and in squa…

math.CO2026

The Erdős-Hajnal High-Girth Subgraph Conjecture Holds in the Polynomial Chromatic-Sparsity Regime

Eric Li

For a graph $G$ put $h_{r} (G) = max χ (H) : H \subseteq G, girth (H) \geq r .$ Erdős and Hajnal asked whether $h_{r} (G) \to \infty$ as $χ (G) \to \infty$ , for every fixed $r \geq 4$ . We…

math.NT2026

Erdős Problem 684 at Density One: Small-prime Parts of Binomial Coefficients and Gaussian Fluctuations

Eric Li

For $0 \leq k \leq n$ , let $u (n, k)$ be the largest divisor of $(k n)$ whose prime factors are at most $k$ . Erdős Problem #684 concerns the special threshold $u (n, k) > n^{2}$ and asks…

math.CO2026

On the Duke--Erdős--Rödl Problem at the One-Third Threshold

Eric Li

Let $G$ be an $n$ -vertex graph with $e (G) \geq n^{2} / k$ . We prove a self-contained internal short-cycle core theorem at the threshold $k \leq n^{1/3}$ : the graph $G$ contains a subgraph…

math.NT2026

Rank Amplification for Shifted Equal Values of Euler's Totient Function

Eric Li

Let $S_{h}^{φ} (x)$ denote the number of integers $n \leq x$ for which $φ (n) = φ (n + h)$ . For the unit shift, we prove $S_{1}^{φ} (x) ≪ x exp - (1/2 - o (1)) lo g x, lo g_{2} x$ . More generally,…

math.NT2026

An Average-Order Theorem for a Shifted Pairwise-Coprime Extremal Problem

Eric Li

For $n \geq 2$ , let $M (n)$ be the supremum of $\sum_{a \in A} 1/ (n - a)$ over pairwise coprime sets $A \subset [1, n)$ . Erdős asked whether $M (n) \leq \sum_{p < n} 1/ p + O (1)$ uniformly in $n$ . We…

The Godsil--McKay Asymptotic for Latin Rectangles in the Sublinear Range of Erdős Problem 725

A Resolution of Erdős Problem 550 on Tree versus Complete Multipartite Ramsey Numbers

A Resolution of Erdős Problem 731 under Dyadic Regularity

A Resolution of Erdős Problems 593 and 1177: Obligatory Triple Systems and Exact Spectra

A Resolution of Erdős Problem 768: the Sylow Divisor Condition

A resolution of Erdős Problem 1061 on the sum-of-divisors function

Prime-Power Rarefaction and a Density-One Lower Bound for Erdős Problem 400

Square-Annular Dynamics and Coalescence Frontiers for n+τ(n)

The Erdős-Hajnal High-Girth Subgraph Conjecture Holds in the Polynomial Chromatic-Sparsity Regime

Erdős Problem 684 at Density One: Small-prime Parts of Binomial Coefficients and Gaussian Fluctuations

On the Duke--Erdős--Rödl Problem at the One-Third Threshold

Rank Amplification for Shifted Equal Values of Euler's Totient Function

An Average-Order Theorem for a Shifted Pairwise-Coprime Extremal Problem

Square-Annular Dynamics and Coalescence Frontiers for $n + τ (n)$