Combinatorially rich sets were introduced by Bergelson and Glasscock (J Comb Theory Ser A 172:105203, 2020) for commutative semigroups and shown to have several properties justifying their name. We extend the definition to arbitrary semigroups and establish the relationships of combinatorially rich sets to other notions of largeness in semigroups.

中文翻译：

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任意半群中的组合丰富集

Bergelson 和 Glasscock (J Comb Theory Ser A 172:105203, 2020) 为交换半群引入了组合富集，并证明其具有多个性质，证明其名称是正确的。我们将定义扩展到任意半群，并建立组合丰富集与半群中其他大概念的关系。