Jeck Lim

activity

20202026

collaborators

14 papers

math.CO2026

On the largest sum-free subset of the lattice cube

Peter Keevash, Jeck Lim

We determine the limiting density of the largest sum-free subset of the lattice cube ${1, 2, \dots, n}^{d}$ for all $d$ , thus resolving the natural conjecture that it is constructed…

cs.AI2026

Human agency in initial human-AI proof formalization workflows

Katherine M. Collins, Simon Frieder, Jonas Bayer +14

For centuries, human mathematicians have written proofs to substantiate their mathematical arguments; yet, the ability to automatically verify the validity of proofs has long been…

math.CO2025

On exponential Freiman dimension

Jeck Lim, Akshat Mudgal, Cosmin Pohoata +1

The exponential Freiman dimension of a finite set $A \subset R^{m}$ , introduced by Green and Tao in 2006, represents the largest positive integer $d$ for which $A$ contain…

math.CO2025

Balancing games on unbounded sets

Imre Bárány, Jeck Lim

For a finite set $V \subset R^{n}$ , a set $T \subset R^{n}$ is called $V$ -closed if $t \in T$ and $v \in V$ imply that either $t + v \in T$ or $t - v \in T$ . The set $P(V):=\…

math.CO2025

Sums of algebraic dilates

David Conlon, Jeck Lim

We show that if $λ_{1}, \dots, λ_{k}$ are algebraic numbers, then $∣ A + λ_{1} \cdot A + \dots + λ_{k} \cdot A ∣ \geq H (λ_{1}, \dots, λ_{k}) ∣ A ∣ - o (∣ A ∣)$ for all finite subsets $A$ of $C$ , where $…

math.CO2025

Evasive sets, twisted varieties, and container-clique trees

Jeck Lim, Jiaxi Nie, Ji Zeng

In the affine space $F_{q}^{n}$ over the finite field of order $q$ , a point set $S$ is said to be $(d, k, r)$ -evasive if the intersection between $S$ and any variety, of dimensi…

math.CO2024

Sums of dilates over groups of prime order

David Conlon, Jeck Lim

For $p$ prime, $A \subseteq Z / p Z$ and $λ \in Z$ , the sum of dilates $A + λ \cdot A$ is defined by \[A + λ\cdot A = \{a + λa' : a, a' \in A\}.\] The basic p…

math.CO2024

On differences of two harmonic numbers

Jeck Lim, Stefan Steinerberger

We prove that the existence of infinitely many $(m_{k}, n_{k}) \in N^{2}$ such that the difference of harmonic numbers $H_{m_{k}} - H_{n_{k}}$ approximates 1 well $$ \lim_{k \righta…

math.CO2023

Everywhere unbalanced configurations

David Conlon, Jeck Lim

An old problem in discrete geometry, originating with Kupitz, asks whether there is a fixed natural number $k$ such that every finite set of points in the plane has a line through…

math.CO2022

Sums of transcendental dilates

David Conlon, Jeck Lim

We show that there is an absolute constant $c > 0$ such that $∣ A + λ \cdot A ∣ \geq e^{c l o g ∣ A ∣} ∣ A ∣$ for any finite subset $A$ of $R$ and any transcendental number $λ\in\…

math.CO2022

Sums of linear transformations

David Conlon, Jeck Lim

We show that if $L_{1}$ and $L_{2}$ are linear transformations from $Z^{d}$ to $Z^{d}$ satisfying certain mild conditions, then, for any finite subset…

math.CO2021

Difference sets in $R^{d}$

David Conlon, Jeck Lim

Let $d \geq 2$ be a natural number. We show that $∣ A - A ∣ \geq (2 d - 2 + \frac{1}{d - 1}) ∣ A ∣ - (2 d^{2} - 4 d + 3)$ for any sufficiently large finite subset $A$ of $R^{d}$ that…

math.CO2021

Fixing a hole

David Conlon, Jeck Lim

We show that any finite $S \subset R^{d}$ in general position has arbitrarily large supersets $T \supseteq S$ in general position with the property that $T$ contains no empt…

math.CO2020

A generalisation of Seymour's second neighbourhood conjecture

Jeck Lim

In this note we propose a generalisation of Seymour's Second Neighbourhood Conjecture to two directed graphs on a vertex set. We prove that this generalisation holds in the case of…

On the largest sum-free subset of the lattice cube

Human agency in initial human-AI proof formalization workflows

On exponential Freiman dimension

Balancing games on unbounded sets

Sums of algebraic dilates

Evasive sets, twisted varieties, and container-clique trees

Sums of dilates over groups of prime order

On differences of two harmonic numbers

Everywhere unbalanced configurations

Sums of transcendental dilates

Sums of linear transformations

Difference sets in Rd

Fixing a hole

A generalisation of Seymour's second neighbourhood conjecture

Difference sets in $R^{d}$