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Number of A$\mathplus$B$ʼne$C solutions in abelian groups and application to counting independent sets in hypergraphsстатья
Дата последнего поиска статьи во внешних источниках: 4 марта 2022 г.
- Авторы: Semchankau Aliaksei, Shabanov Dmitry, Shkredov Ilya
- Журнал: European Journal of Combinatorics
- Том: 100
- Год издания: 2022
- Издательство: Academic Press
- Местоположение издательства: United States
- Первая страница: 103453
- DOI: 10.1016/j.ejc.2021.103453
- Аннотация: The paper deals with a problem of Additive Combinatorics. Let G be a finite abelian group of order N. We prove that the number of subset triples A,B,C⊂G such that for any x∈A, y∈B and z∈C one has x+y≠z equals3⋅4N+N3N+1+O((3−c∗)N)for some absolute constant c∗>0. This provides a tight estimate for the number of independent sets in a special 3-uniform linear hypergraph and gives a support for the natural conjecture concerning the maximal possible number of independent sets in such hypergraphs on n vertices.https://doi.org/10.1016/j.ejc.2021.103453
- Добавил в систему: Семченков Алексей Сергеевич