4 papers
Explicit Fractalizers: Prime-Order Paley Graphs and other Cayley Graphs
Aldo Kiem, Fan Wei
The inducibility problem asks for the maximum number of induced copies of a fixed graph among all graphs with a prescribed number of vertices. Inducibility has been an active area…
Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?
Konrad Mundinger, Max Zimmer, Aldo Kiem +2
We demonstrate how neural networks can drive mathematical discovery through a case study of the Hadwiger-Nelson problem, a long-standing open problem at the intersection of discret…
Adjunctions, Box Products, and Forcing Families
Aldo Kiem, Olaf Parczyk, Christoph Spiegel
Sidorenko's conjecture states that the number of copies of any given bipartite graph in another graph of given density is asymptotically minimized by a random graph. For bipartite…
The Four-Color Ramsey Multiplicity of Triangles
Aldo Kiem, Sebastian Pokutta, Christoph Spiegel
We study a generalization of a famous result of Goodman and establish that asymptotically at least a fraction of all triangles needs to be monochromatic in any four-colorin…