论文标题
二进制操作的关联频谱
The associative-commutative spectrum of a binary operation
论文作者
论文摘要
我们启动了针对二元操作失败的定量度量的研究。我们将此度量称为关联频谱，因为它扩展了所谓的关联频谱（也称为亚缔合性类型），该频谱衡量了二进制操作的非缔合性。实际上，关联交通频谱（分别的关联频谱）是对称（分别的非对称）手术的基数，该基础是自然自然地从群体（带有二进制操作的集合）获得的。在本文中，我们为关联频谱提供了一些一般结果，可以准确确定某些二进制操作的措施，并提出一些问题以供将来的研究。
We initiate the study of a quantitative measure for the failure of a binary operation to be commutative and associative. We call this measure the associative-commutative spectrum as it extends the so-called associative spectrum (also known as the subassociativity type), which measures the nonassociativity of a binary operation. In fact, the associative-commutative spectrum (resp. associative spectrum) is the cardinality of the symmetric (resp. nonsymmetric) operad obtained naturally from a groupoid (a set with a binary operation). In this paper we provide some general results on the associative-commutative spectrum, precisely determine this measure for certain binary operations, and propose some problems for future study.
