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- W2965611217 abstract "This paper generalizes the basic notions of additive and multiplicative combinatorics to the setting of group actions: if $G$ is a group acting on a set $X$, and we have subsets $Asubseteq G$ and $Ysubseteq X$ such that the set of pairs $gcdot y$ with $gin A,yin Y$ is not much larger than $Y$, what structure must $A$ and $Y$ have? Briefly, what is the structure of sets with small set? In this setting, we develop analogs of Ruzsa's triangle inequality, covering theorems, multiplicative energy, and the Balog-Szemeredi-Gowers theorem. Approximate stabilizers, which we call symmetry sets, play an important role. While our focus is on presenting a general theory, we answer the inverse image set question in some special cases. To do so, we combine the group action version of the Balog-Szemeredi-Gowers theorem with structure theorems for approximate groups and bounds for the sizes of symmetry sets." @default.
- W2965611217 created "2019-08-13" @default.
- W2965611217 creator A5075932839 @default.
- W2965611217 date "2019-07-31" @default.
- W2965611217 modified "2023-09-27" @default.
- W2965611217 title "Group Action Combinatorics" @default.
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