Generators and ranks in finite partial transformation semigroups
G. U. Garba, Abdussamad Tanko Imam · The scientific electronic library of periodicals of the National Academy of Sciences of Ukraine (National Academy of Sciences of Ukraine) · 2017
We extend the concept of path-cycle, to the semigroup Pn, of all partial maps on Xn={1,2,…,n}, and show that the classical decomposition of permutations into disjoint cycles can be extended to elements of Pn by means of path-cycles. The device is used to obtain information about generating sets for the semigroup Pn\\Sn, of all singular partial maps of Xn. Moreover, we give a definition for the (m,r)-rank of Pn\\Sn and show that it is n(n+1)/2.