  Recent work in hypergraph Ramsey theory has involved the introduction of a
"lifting map" that associates a certain $3$-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 $3$-uniform hypergraph Ramsey
numbers.

Combinatorics