The associative-commutative spectrum of a binary operation

Huang, Jia; Lehtonen, Erkko

http://hdl.handle.net/10362/155424

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Autores

Huang, Jia

Lehtonen, Erkko

Resumo(s)

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 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 operad with (resp. without) permutations 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.