Abstract
Let G be an abelian group of bounded exponent and A ⊆ G. We show that if the collection of translates of A has VC dimension at most d, then for every ε > 0 there is a subgroup H of G of index at most ε-d-o(1) such that one can add or delete at most ejGj elements to/from A to make it a union of H-cosets.
Original language | English (US) |
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Article number | 3 |
Journal | Discrete Analysis |
Volume | 2019 |
DOIs | |
State | Published - 2019 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology
- Discrete Mathematics and Combinatorics
Keywords
- Arithmetic regularity
- Induced patterns
- Property testing
- Regularity lemma
- Removal lemma
- Vc dimension