Algebraic Properties of a Hypergraph Lifting Map
arXiv:2012.13500
Abstract
Recent work in hypergraph Ramsey theory has involved the introduction of a "lifting map" that associates a certain -uniform hypergraph to a given graph, bounding cliques in a predictable way. In this paper, we interpret the lifting map as a linear transformation. This interpretation allows us to use algebraic techniques to prove several structural properties of the lifting map, culminating in new lower bounds for certain -uniform hypergraph Ramsey numbers.
8 pages, 0 figures