Induced arithmetic removal: complexity 1 patterns over finite fields

Abstract

We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that given a fixed collection of $r$-colored complexity 1 arithmetic patterns over ${\mathbb{F}}_q$, every coloring $\varphi :{\mathbb{F}}_q^n\setminus \{0\}\to [r]$ with $o(1)$ density of every such pattern can be recolored on an $o(1)$-fraction of the space so that no such pattern remains.

22 pages

References in corpus (3)

• A Szemeredi-type regularity lemma in abelian groups, with applications
• Fourier uniformity on subspaces
• Good Bounds in Certain Systems of True Complexity One

Cited by in corpus (2)

• Testing linear-invariant properties
• Induced arithmetic removal for partition-regular patterns of complexity 1