5 papers
The Mathieu group is a Galois group over
Xiaoyu Huang, Blake Jackson, Kyu-Hwan Lee +3
Researchers studying the inverse Galois problem realized 25 of the 26 sporadic finite simple groups as Galois groups over during 1984--1989. We complete this program b…
Discovering a Zeta Map Algorithm on Dyck Paths via Mechanistic Interpretability
Xiaoyu Huang, Blake Jackson, Kyu-Hwan Lee
Machine learning is increasingly used in mathematical discovery, but in mathematics the desired output is often not a prediction itself, but an explicit construction that can be ch…
Lean-GAP: A Dataset of Formalized Graduate Algebra Problems
Seewoo Lee, Byung-Hak Hwang, Hyojae Lim +10
We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pi…
From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithm
Xiaoyu Huang, Blake Jackson, Kyu-Hwan Lee
There is a large class of problems in algebraic combinatorics which can be distilled into the same challenge: construct an explicit combinatorial bijection. Traditionally, research…
Machine Learning Mutation-Acyclicity of Quivers
Kymani T. K. Armstrong-Williams, Edward Hirst, Blake Jackson +1
Machine learning (ML) has emerged as a powerful tool in mathematical research in recent years. This paper applies ML techniques to the study of quivers -- a type of directed multig…