We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on abelian equivalence, which is the equivalence relation defined in the set of words by having the same Parikh vector, that is, the same number of occurrences of each letter of the alphabet. In the past few years, there was a lot of research on abelian analogues of classical definitions and properties in combinatorics on words. This survey aims to gather these results.

中文翻译：

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单词的阿贝尔组合学：一项调查

我们调查了单词交换组合学中的已知结果和未解决的问题。词的阿贝尔组合是对词组合的经典理论的交换设置的扩展。扩展基于阿贝尔等价，这是通过具有相同的 Parikh 向量（即字母表中每个字母的相同出现次数）在词集中定义的等价关系。在过去的几年里，有很多关于词组合学中经典定义和性质的阿贝尔类比的研究。本次调查旨在收集这些结果。