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

2018/11/11 by Peter M. Higgins, Higgins, Peter M.
Computer Science · #20M17 #20M18 #20M20 #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1811.04472

openalex publication_date 2018/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We continue the study of permutations of a finite regular semigroup that map\neach element to one of its inverses, providing a complete description in the\ncase of semigroups whose idempotent generated subsemigroup is a union of\ngroups. We show, in two ways, how to construct an involution matching on the\nsemigroup of all transformations which either preserve or reverse orientation\nof a finite cycle. Finally, by way of application, we prove that finite full\ntransformation semigroups have no cover by inverse semigroups that is closed\nunder intersection.\n

Related

• Finite regular semigroups with permutations that map elements to inverses
• A new formulation of the semigroup of orientation-preserving and\n orientation-reversing mappings
• Orientation-preserving and orientation-reversing mappings: a new description
• Varieties of Boolean inverse semigroups
• Transitive representations of inverse semigroups