On Linear Configurations in Subsets of Compact Abelian Groups, and Invariant Measurable Hypergraphs
  • Metaadatok
Tartalom: http://real.mtak.hu/44224/
Archívum: MTA Könyvtár
Gyűjtemény: Status = Published

Type = Article
Cím:
On Linear Configurations in Subsets of Compact Abelian Groups, and Invariant Measurable Hypergraphs
Létrehozó:
Candela, P.
Szegedy, BalĂĄzs
Vena, L.
Kiadó:
Springer-Verlag
Dátum:
2016
Téma:
QA Mathematics / matematika
QA166-QA166.245 Graphs theory / grĂĄfelmĂŠlet
Tartalmi leírás:
We prove an arithmetic removal result for all compact abelian groups, generalizing a finitary removal result of Král’, Serra, and the third author. To this end, we consider infinite measurable hypergraphs that are invariant under certain group actions, and for these hypergraphs we prove a symmetry-preserving removal lemma, which extends a finitary result of the same name by the second author. We deduce our arithmetic removal result by applying this lemma to a specific type of invariant measurable hypergraph. As a direct consequence of our removal result, we obtain the following generalization of Szemerédi’s theorem: for any compact abelian group G, any measurable set A⊆ G with Haar probability μ(A) ≥ α> 0 satisfies ∫G∫G1A(x)1A(x+r)..1A(x+(k-1)r)dμ(x)dμ(r)≥c, where the constant c= c(α, k) > 0 is valid uniformly for all G. This result is shown to hold more generally for any translationinvariant system of r linear equations given by an integer matrix with coprime r× r minors. © 2016, Springer International Publishing.
Nyelv:
angol
magyar
Típus:
Article
PeerReviewed
info:eu-repo/semantics/article
Formátum:
text
text
Azonosító:
Candela, P. and Szegedy, BalĂĄzs and Vena, L. (2016) On Linear Configurations in Subsets of Compact Abelian Groups, and Invariant Measurable Hypergraphs. ANNALS OF COMBINATORICS, 20 (3). pp. 487-524. ISSN 0218-0006
Kapcsolat:
MTMT:3155624; doi:10.1007/s00026-016-0313-1