Efficient arithmetic regularity and removal lemmas for induced bipartite patterns
Abstract
Let $G$ be an abelian group of bounded exponent and $A \subseteq G$. We show that if the collection of translates of $A$ has VC dimension at most $d$, then for every $\epsilon>0$ there is a subgroup $H$ of $G$ of index at most $\epsilon^{do(1)}$ such that one can add or delete at most $\epsilonG$ elements to/from $A$ to make it a union of $H$cosets. We also establish a removal lemma with polynomial bounds, with applications to property testing, for induced bipartite patterns in a finite abelian group with bounded exponent.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 arXiv:
 arXiv:1801.04675
 Bibcode:
 2018arXiv180104675A
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 Discrete Analysis 2019:3, 14 pp