On the removal lemma for linear systems over Abelian groups

Authors:
Daniel KráL';Oriol Serra;LluíS Vena
Affiliations:
Computer Science Institute, Faculty of Mathematics and Physics, Charles University, Czech Republic;Departament de Matemítica Aplicada IV, Universitat Politècnica de Catalunya, Spain;Department of Mathematics, University of Toronto, Canada
Venue:
European Journal of Combinatorics
Year:
2013

Citing 4
Cited 1

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Note: A combinatorial proof of the Removal Lemma for Groups

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Testability and repair of hereditary hypergraph properties

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On the number of monochromatic solutions of integer linear systems on abelian groups

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Abstract

In this paper we present an extension of the removal lemma to integer linear systems over abelian groups. We prove that, if the k-determinantal of an integer (kxm) matrix A is coprime with the order n of a group G and the number of solutions of the system Ax=b with x"1@?X"1,...,x"m@?X"m is o(n^m^-^k), then we can eliminate o(n) elements in each set to remove all these solutions.