4 papers
On Hales-Jewett and Related Numbers
Nathan Conlon, Nayda Farnsworth, Aaron Robertson
We investigate the Hales-Jewett numbers and some variants of them, both computationally and via enumerative and probabilistic arguments. In particular, we give the improved lower b…
A Note on Conjectures of Gullerud, Johnson, and Mbirika
Robert Davis, Nayda Farnsworth
In 2023, Gullerud, Johnson, and Mbirika presented results on their study of certain tridiagonal real symmetric matrices. As part of their work, they studied the roots to nonhomogen…
Elimination Without Eliminating: Computing Complements of Real Hypersurfaces Using Pseudo-Witness Sets
Paul Breiding, John Cobb, Aviva K. Englander +6
Many hypersurfaces in algebraic geometry, such as discriminants, arise as the projection of another variety. The real complement of such a hypersurface partitions its ambient space…
Can Neural Networks Learn Small Algebraic Worlds? An Investigation Into the Group-theoretic Structures Learned By Narrow Models Trained To Predict Group Operations
Henry Kvinge, Andrew Aguilar, Nayda Farnsworth +4
While a real-world research program in mathematics may be guided by a motivating question, the process of mathematical discovery is typically open-ended. Ideally, exploration neede…