3 papers
math.CO2026
A 21-Coloring of the Plane Without Monochromatic Unit-Area Rectangles
Gary Hu, Yumo Liu
Erdős and Graham asked whether every finite coloring of the plane must contain a monochromatic rectangle of any prescribed area. Kovač gave a negative answer by constructing a …
math.CO2025
Lower Bounds on Intersection Families for Certain Graphs
Paul Hamrick, Gary Hu
A family of graphs is -intersecting if the edge intersection of any two graphs in contains a copy of a fixed graph . A fundamental problem is to d…
math.RT2025
Spectral Equivalence of Solvable Lie Algebras with Nilradical I: General and Heisenberg Cases
Gary Hu
Building on the work of Yang, Key, and Muller, we investigate the spectral theory of solvable Lie algebras through their characteristic polynomials and associated spectral invarian…