Selected Results in Additive Combinatorics: An Exposition
نویسنده
چکیده
We give a stripped-down, self-contained exposition of selected results in additive combinatorics over the vector space F2, leading to the result by Samorodnitsky (STOC 2007) stating that linear transformations are efficiently testable. In particular, we prove the theorems known as the Balog-Szemerédi-Gowers theorem (Combinatorica 1994 and GAFA 1998) and the Freiman-Ruzsa theorem (AMS 1973 and Astérisque 1999). ACM Classification: 05D99 AMS Classification: F.1.2, F.2.2
منابع مشابه
Selected Results in Additive Combinatorics: An Exposition (Preliminary Version)
We give a self-contained exposition of selected results in additive combinatorics over the group GF (2)n = {0, 1}n. In particular, we prove the celebrated theorems known as the Balog-Szemeredi-Gowers theorem (’94 and ’98) and the Freiman-Ruzsa theorem (’73 and ’99), leading to the remarkable result by Samorodnitsky (’07) that linear transformations are efficiently testable. No new result is pro...
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عنوان ژورنال:
- Theory of Computing, Graduate Surveys
دوره 3 شماره
صفحات -
تاریخ انتشار 2007