Conjugacy Classes in Order- Preserving Transformation Semi groups with Injective Contraction
Year: 2024
Type: article
Abstract: Enumerating the elements within transformation semigroups poses a significant challenge. Prior knowledge has been more on the injective order-preserving and order-decreasing transformation semigroup, a sub-semigroup of the injective transformation semigroup. This work categorized elements within the injective order-preserving sub-semigroup with contraction, arranging them into conjugacy classes using a path decomposition approach based on circuit and proper paths. Furthermore, these conjugacy classes were organized according to the number of images. A general expression was derived for the number of conjugacy classes in the injective order-preserving contraction transformation semigroup. We found that the number of conjugacy classes in this transformation is precisely given by the sequence A000070 (OEIS). This alignment suggests a profound relationship between the structure of these transformations and the theory of partitions (number theory), opening up new avenues for research and analysis.
DOI: 10.61448/njse223243
Authors: J.O. Emunefe, A.O. Atonuje, J Tsetimi,
Institutions: Delta State University, Petroleum Training Institute
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4405625906