On the Number of Conjugacy Classes in the Injective Order-Decreasing Transformation Semigroup.
Ifeanyichukwu Jeff Ugbene, Everestus Obinwanne Eze, S. O. Makanjuola, Michael Obinna Okpara · 2013
One of the problems we face in transformation semigroups is its enumeration (Umar, 2010). The injective order-decreasing transformation semigroup is a sub-semigroup of injective transformation semigroup. Its elements were studied and arranged in their respective conjugacy class while applying the use of two kinds of path structure (the Circuit and Proper path) in its path decomposition. The conjugacy classes were also arranged according to the number of its images in any number of the Injective order-decreasing transformation Semigroup. A general expression was obtained for the number of conjugacy classes in the orderdecreasing transformation semigroup.