Work

On the monoid of order-preserving transformations of a finite chain whose ranges are intervals

Year: 2024

Type: article

Abstract: We give a presentation for the monoid $$\mathscr{I}\mathscr{O}_n$$ I O n of all order-preserving transformations of an n-chain whose ranges are intervals. We also consider the submonoid $$\mathscr{I}\mathscr{O}_n^-$$ I O n - of $$\mathscr{I}\mathscr{O}_n$$ I O n consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.

Source: Semigroup Forum

DOI: 10.1007/s00233-024-10466-2

Author: Vítor H. Fernandes

Institution: Universidade Nova de Lisboa

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Universidade Nova de Lisboa, Fundação para a Ciência e a Tecnologia