Involution matchings, the semigroup of orientation-preserving and orientation-reversing mappings, and inverse covers of the full transformation semigroup

Content Provider	Semantic Scholar
Author	Higgins, Peter M.
Copyright Year	2018
Abstract	We continue the study of permutations of a finite regular semigroup that map each element to one of its inverses, providing a complete description in the case of semigroups whose idempotent generated subsemigroup is a union of groups. We show, in two ways, how to construct an involution matching on the semigroup of all transformations which either preserve or reverse orientation of a cycle. Finally, as an application, we use involution matchings to prove that when the base set has at least four members, a finite full transformation semigroup has no cover by inverse subsemigroups that is closed under intersection.
Starting Page	669
Ending Page	689
Page Count	21
File Format	PDF HTM / HTML
DOI	10.1007/s00233-019-10018-z
Volume Number	98
Alternate Webpage(s)	https://arxiv.org/pdf/1811.04472v2.pdf
Alternate Webpage(s)	https://doi.org/10.1007/s00233-019-10018-z
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article