Pseudo-Random Hypergraphs

We study the interplay between notions of quasi-randomness for hypergraphs. In particular, we show a strong connection between discrepancy-type measures of quasirandomness in the hypergraph setting. Exploiting this connection, we provide a long list of disparate quasirandom properties and show that these properties are all equivalent (in the sense of Chung, Graham, and Wilson) with polynomial bounds on their interdependences.