On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range

Abstract

Let X be an infinite linearly ordered set and let Y be a nonempty subset of X. We calculate the relative rank of the semigroup $\mathcal{O}\mathcal{P}(X,Y)$ of all orientation-preserving transformations on X with restricted range Y modulo the semigroup $\mathcal{O}(X,Y)$ of all order-preserving transformations on X with restricted range Y. For Y = X, we characterize the relative generating sets of minimal size.

Keywords:

• Order-preserving transformations
• orientation-preserving transformations
• relative rank
• restricted range
• transformation semigroups on infinite chain

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20M20

Additional information

Funding

Ilinka Dimitrova gratefully acknowledges support of DAAD, within the funding programme “Research Stays for University Academics and Scientists, 2019” number 57442043.