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 |
| _version_ | 1826189974709469184 |
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| author | Fox, Jacob Tidor, Jonathan Zhao, Yufei |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Fox, Jacob Tidor, Jonathan Zhao, Yufei |
| author_sort | Fox, Jacob |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T08:33:06Z |
| format | Article |
| id | mit-1721.1/145896 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:33:06Z |
| publishDate | 2022 |
| publisher | Springer Science and Business Media LLC |
| record_format | dspace |
| spelling | mit-1721.1/1458962023-03-09T05:27:38Z Induced arithmetic removal: complexity 1 patterns over finite fields Fox, Jacob Tidor, Jonathan Zhao, Yufei Massachusetts Institute of Technology. Department of Mathematics 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. 2022-10-18T17:21:28Z 2022-10-18T17:21:28Z 2022 2022-10-18T17:17:26Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/145896 Fox, Jacob, Tidor, Jonathan and Zhao, Yufei. 2022. "Induced arithmetic removal: complexity 1 patterns over finite fields." Israel Journal of Mathematics, 248 (1). en 10.1007/S11856-022-2290-X Israel Journal of Mathematics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer Science and Business Media LLC arXiv |
| spellingShingle | Fox, Jacob Tidor, Jonathan Zhao, Yufei Induced arithmetic removal: complexity 1 patterns over finite fields |
| title | Induced arithmetic removal: complexity 1 patterns over finite fields |
| title_full | Induced arithmetic removal: complexity 1 patterns over finite fields |
| title_fullStr | Induced arithmetic removal: complexity 1 patterns over finite fields |
| title_full_unstemmed | Induced arithmetic removal: complexity 1 patterns over finite fields |
| title_short | Induced arithmetic removal: complexity 1 patterns over finite fields |
| title_sort | induced arithmetic removal complexity 1 patterns over finite fields |
| url | https://hdl.handle.net/1721.1/145896 |
| work_keys_str_mv | AT foxjacob inducedarithmeticremovalcomplexity1patternsoverfinitefields AT tidorjonathan inducedarithmeticremovalcomplexity1patternsoverfinitefields AT zhaoyufei inducedarithmeticremovalcomplexity1patternsoverfinitefields |