Efficient arithmetic regularity and removal lemmas for induced bipartite patterns
Name
1801.04675.pdf
Description
Published version
Size
298.82 KB
Format
Adobe PDF
Checksum (MD5)
0ffdb8cb1659016f53bad4a52a9ad85f
Author(s)
Alon, Noga
Fox, Jacob
Zhao, Yufei
Date Issued
April 12, 2019
Journal
Discrete Analysis 2019:3, 14 pp
Publisher
Alliance of Diamond Open Access Journals
Citation
Alon, Noga, Fox, Jacob and Zhao, Yufei. 2019. "Efficient arithmetic regularity and removal lemmas for induced bipartite patterns." Discrete Analysis 2019:3, 14 pp, 2019 (03).
Version
Final published version
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
$\epsilon^{-d-o(1)}$ such that one can add or delete at most $\epsilon|G|$
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.19086/da.7757
