Combinatorial results for semigroups of order-preserving partial transformations

By Abdallah Laradji, Abdullahi Umar. 2004

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Abstract Let PO n be the semigroup of all order-preserving partial transformations of a finite chain. It is shown that | PO n |=c n satisfies the recurrence (2n−1)(n+1)c n+1 =4 3n 2 −1 c n −(2n+1)(n−1)c n−1 with initial conditions c0=1, c1=2. It is also shown that |E( PO n )|=e n satisfies the recurrence en+1=5(en−en−1)+1 with initial conditions e0=1, e1=2. Moreover, the cardinalities of the Green's relations L , R and J have been computed.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/62c2d78960349b9e3ba8770971996ff88fa4da06