9 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 by…
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…
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…
A geometric model for the non--rigid modules of type
Blake Jackson
We give a geometric model for the non--rigid modules over acyclic path algebras of type . Similar models have been provided for module categories over path alge…
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…
Geometry of -vectors and -Matrices for Mutation-Infinite Quivers
Tucker J. Ervin, Blake Jackson, Kyungyong Lee +1
The set of forks is a class of quivers introduced by M. Warkentin, where every connected mutation-infinite quiver is mutation equivalent to infinitely many forks. Let be a fork…
A topology on the poset of quiver mutation classes
Tucker J. Ervin, Blake Jackson
To better understand mutation-invariant and hereditary properties of quivers (and more generally skew-symmetrizable matrices), we have constructed a topology on the set of all muta…
Permutations whose reverse shares the same recording tableau in the RSK correspondence
Tucker J. Ervin, Blake Jackson, Jay Lane +4
The RSK correspondence is a bijection between permutations and pairs of standard Young tableaux with identical shape, where the tableaux are commonly denoted (insertion) and $Q…
Mutations of reflections and existence of pseudo-acyclic orderings for type
Tucker J. Ervin, Blake Jackson, Kyu-Hwan Lee +1
In a recent paper by K.-H. Lee, K. Lee and M. Mills, a mutation of reflections in the universal Coxeter group is defined in association with a mutation of a quiver. A matrix repres…