William J. Wesley

activity

20242026

collaborators

3 papers

cs.AI2026

Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment

Stephen Chung, Wenyu Du, William J. Wesley

We study autonomous mathematical discovery in the Station, an open-world multi-agent environment in which AI agents from different model families pursue a shared research goal with…

math.CO2025

Ramsey Numbers through the Lenses of Polynomial Ideals and NullstellensÃ¤tze

JesÃºs A. De Loera, William J. Wesley

In this article we study the Ramsey numbers $R (r, s)$ through Hilbert's Nullstellensatz and Alon's Combinatorial Nullstellensatz. We give polynomial encodings whose solutions corres…

math.CO2024

Optimization Tools for Computing Colorings of $[1, \dots, n]$ with Few Monochromatic Solutions on $3$ -variable Linear Equations

JesÃºs A. De Loera, Denae Ventura, Liuyue Wang +1

A famous result in arithmetic Ramsey theory says that for many linear homogeneous equations $E$ there is a threshold value $R_{k} (E)$ (the Rado number of $E$ ) such that for any $k$ -c…

Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment

Ramsey Numbers through the Lenses of Polynomial Ideals and NullstellensÃ¤tze

Optimization Tools for Computing Colorings of [1,⋯,n] with Few Monochromatic Solutions on 3-variable Linear Equations

Optimization Tools for Computing Colorings of $[1, \dots, n]$ with Few Monochromatic Solutions on $3$ -variable Linear Equations