A Removal Lemma for Systems of Linear Equations over Finite Fields
| dc.creator | Král', Dan | |
| dc.creator | Serra, Oriol | |
| dc.creator | Vena, Lluís | |
| dc.date | 2008-09-10 | |
| dc.date.accessioned | 2026-07-07T10:02:04Z | |
| dc.date.available | 2026-07-07T10:02:04Z | |
| dc.description | We prove a removal lemma for systems of linear equations over finite fields: let $X_1,...,X_m$ be subsets of the finite field $\F_q$ and let $A$ be a $(k\times m)$ matrix with coefficients in $\F_q$ and rank $k$; if the linear system $Ax=b$ has $o(q^{m-k})$ solutions with $x_i\in X_i$, then we can destroy 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. | |
| dc.identifier | https://arxiv.org/abs/0809.1846 | |
| dc.identifier | http://arxiv.org/abs/0809.1846 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168845 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.title | A Removal Lemma for Systems of Linear Equations over Finite Fields | |
| dc.type | text |