Freiman homomorphisms on sparse random sets
A result of Fiz Pontiveros shows that if A is a random subset of ZN where each element is chosen independently with probability N −1/2+o(1), then with high probability every Freiman homomorphism defined on A can be extended to a Freiman homomorphism on the whole of ZN . In this paper we improve the...
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| Format: | Journal article |
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Oxford University Press
2017
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| _version_ | 1797096698893303808 |
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| author | Conlon, D Gowers, W |
| author_facet | Conlon, D Gowers, W |
| author_sort | Conlon, D |
| collection | OXFORD |
| description | A result of Fiz Pontiveros shows that if A is a random subset of ZN where each element is chosen independently with probability N −1/2+o(1), then with high probability every Freiman homomorphism defined on A can be extended to a Freiman homomorphism on the whole of ZN . In this paper we improve the bound to CN −2/3(log N)1/3, which is best possible up to the constant factor. |
| first_indexed | 2024-03-07T04:45:15Z |
| format | Journal article |
| id | oxford-uuid:d306eedc-7239-4613-87a4-781f01d1519c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:45:15Z |
| publishDate | 2017 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:d306eedc-7239-4613-87a4-781f01d1519c2022-03-27T08:08:24ZFreiman homomorphisms on sparse random setsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d306eedc-7239-4613-87a4-781f01d1519cSymplectic Elements at OxfordOxford University Press2017Conlon, DGowers, WA result of Fiz Pontiveros shows that if A is a random subset of ZN where each element is chosen independently with probability N −1/2+o(1), then with high probability every Freiman homomorphism defined on A can be extended to a Freiman homomorphism on the whole of ZN . In this paper we improve the bound to CN −2/3(log N)1/3, which is best possible up to the constant factor. |
| spellingShingle | Conlon, D Gowers, W Freiman homomorphisms on sparse random sets |
| title | Freiman homomorphisms on sparse random sets |
| title_full | Freiman homomorphisms on sparse random sets |
| title_fullStr | Freiman homomorphisms on sparse random sets |
| title_full_unstemmed | Freiman homomorphisms on sparse random sets |
| title_short | Freiman homomorphisms on sparse random sets |
| title_sort | freiman homomorphisms on sparse random sets |
| work_keys_str_mv | AT conlond freimanhomomorphismsonsparserandomsets AT gowersw freimanhomomorphismsonsparserandomsets |