Combinatorics in the exterior algebra and the Bollobás Two Families Theorem

Alex Scott, Elizabeth Wilmer

Published 2019-07-13Version 1

We investigate the combinatorial structure of subspaces of the exterior algebra of a finite-dimensional real vector space, working in parallel with the extremal combinatorics of hypergraphs. As an application, we prove a new extension of the Two Families Theorem of Bollob\'{a}s.