$L_p$ regular sparse hypergraphs: box norms
Combinatorics
2021-01-29 v3 Functional Analysis
Probability
Abstract
We consider some variants of the Gowers box norms, introduced by Hatami, and show their relevance in the context of sparse hypergraphs. Our main results are the following. Firstly, we prove a generalized von Neumann theorem for graphons. Secondly, we give natural examples of pseudorandom families, that is, sparse weighted uniform hypergraphs which satisfy relative versions of the counting and removal lemmas.
Keywords
Cite
@article{arxiv.1510.07140,
title = {$L_p$ regular sparse hypergraphs: box norms},
author = {Pandelis Dodos and Vassilis Kanellopoulos and Thodoris Karageorgos},
journal= {arXiv preprint arXiv:1510.07140},
year = {2021}
}