Informace o publikaci
A removal lemma for systems of linear equations over finite fields
| Autoři | |
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| Rok publikování | 2012 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Israel Journal of Mathematics |
| Citace | KRÁĽ, Daniel, O SERRA a L VENA. A removal lemma for systems of linear equations over finite fields. Israel Journal of Mathematics. JERUSALEM: HEBREW UNIV MAGNES PRESS, 2012, roč. 187, č. 1, s. 193-207. ISSN 0021-2172. Dostupné z: https://dx.doi.org/10.1007/s11856-011-0080-y. |
| Doi | http://dx.doi.org/10.1007/s11856-011-0080-y |
| Popis | We prove a removal lemma for systems of linear equations over finite fields: let X (1), aEuro broken vertical bar, X (m) be subsets of the finite field F (q) and let A be a (k x m) matrix with coefficients in F (q) ; if the linear system Ax = b has o(q (m-k) ) solutions with x (i) a X (i) , then we can eliminate all these solutions by deleting o(q) elements from each X (i) . This extends a result of Green [Geometric and Functional Analysis 15 (2) (2005), 340-376] for a single linear equation in abelian groups to systems of linear equations. In particular, we also obtain an analogous result for systems of equations over integers, a result conjectured by Green. Our proof uses the colored version of the hypergraph Removal Lemma. |