On the removal lemma for linear systems over Abelian groups

被引：9

作者：

Kral, Daniel ^{[1
]}

Serra, Oriol ^{[2
]}

Vena, Lluis ^{[3
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Inst Comp Sci, CR-11636 Prague 1, Czech Republic

[2] Univ Politecn Cataluna, Dept Matemat Aplicada 4, E-08028 Barcelona, Spain

[3] Univ Toronto, Dept Math, Toronto, ON M5S 1A1, Canada

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2013年 / 34卷 / 02期

基金：

欧洲研究理事会;

关键词：

PARTIAL INTEGRAL MATRIX; UNIFORM HYPERGRAPHS; UNIMODULAR MATRIX; REGULARITY LEMMA; COMPLETION;

D O I：

10.1016/j.ejc.2012.07.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 (k x m) 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) is an element of X-1, . . . , x(m) is an element of X-m, is o(n(m-k)), then we can eliminate o(n) elements in each set to remove all these solutions. (c) 2012 Elsevier Ltd. All rights reserved.

引用

页码：248 / 259

页数：12

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