4 papers
Improved lower bounds for the Shannon capacity of odd cycles
Nathaniel Itty, Christopher D. Rosin, Chase Carstensen +1
The Shannon capacity of a graph quantifies the maximum rate at which information can be transmitted with zero error over a noisy channel. It is lower bounded by $α(G^d)^…
Improved Upper Bounds for Slicing the Hypercube
Duncan Soiffer, Nathaniel Itty, Christopher D. Rosin +5
A collection of hyperplanes slices all edges of the -dimensional hypercube with vertex set if, for every edge in the hypercube, there exists…
The Karp Dataset
Mason DiCicco, Eamon Worden, Conner Olsen +3
Understanding the mathematical reasoning capabilities of Large Language Models (LLMs) is a central topic in the study of artificial intelligence. This new domain necessitates the c…
Nearest Neighbor Complexity and Boolean Circuits
Mason DiCicco, Vladimir Podolskii, Daniel Reichman
A nearest neighbor representation of a Boolean function is a set of vectors (anchors) labeled by or such that if and only if the closest anchor to $\ve…