3 citations · 5 across the 11 of their papers we have counts for
9 papers · 1 filter
A new formulation of the semigroup of orientation-preserving and orientation-reversing mappings
Peter M. Higgins, Alexei Vernitski
We characterize the respective semigroups of mappings that preserve, or that preserve or reverse orientation of a finite cycle, in terms of their actions on oriented triples and or…
Epimorphisms, dominions and H-commutative semigroups
Peter M. Higgins, Noor Alam, Noor Mohammad Khan
In the present paper, a series of results and examples that explore the structural features of H-commutative semigroups are provided. We also generalise a result of Isbell from com…
Green's relations and stability for subsemigroups
James East, Peter M. Higgins
We prove new results on inheritance of Green's relations by subsemigroups in the presence of stability of elements. We provide counterexamples in other cases to show in particular…
Burrows-Wheeler transformations and de Bruijn words
Peter M. Higgins
We formulate and explain the extended Burrows-Wheeler transform of Mantaci et al from the viewpoint of permutations on a chain taken as a union of partial order-preserving mappings…
Embedding in a finite 2-generator semigroup
Peter M. Higgins
We augment the body of existing results on embedding finite semigroups of a certain type into 2-generator finite semigroups of the same type. The approach adopted applies to finite…
Permutations of a semigroup that map to inverses
Peter M. Higgins
We investigate the question as to when the members of a finite regular semigroup may be permuted in such a way that each member is mapped to one of its inverses. In general this is…
Orthodox semigroups and permutation matchings
Peter M. Higgins
We determine when an orthodox semigroup S has a permutation that sends each member of S to one of its inverses and show that if such a permutation exists, it may be taken to be an…
Involution matchings, the semigroup of orientation-preserving and orientation-reversing mappings, and inverse covers of the full transformation semigroup
Peter M. Higgins
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 i…
Algebras defined by equations
Peter M Higgins, Marcel Jackson
We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (gener…