Induced arithmetic removal: complexity 1 patterns over finite fields
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 $\phi \colon \mathbb F_q^n \setminus\{0\} \t...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Science and Business Media LLC
2022
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| Online Access: | https://hdl.handle.net/1721.1/145896 |
| Summary: | 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 $\phi \colon \mathbb F_q^n \setminus\{0\} \to
[r]$ 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. |
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