Combinatorial results for semigroups of order-preserving partial transformations

• DOI: 10.1016/j.jalgebra.2003.10.023
• Publication Date: 2004-01-27T10:22:43Z
• Authors: A Laradji; A Umar
• Keywords: Algebra and Number Theory; 0101 mathematics; 01 natural sciences

AbstractLet POn be the semigroup of all order-preserving partial transformations of a finite chain. It is shown that |POn|=cn satisfies the recurrence (2n−1)(n+1)cn+1=43n2−1cn−(2n+1)(n−1)cn−1 with initial conditions c0=1, c1=2. It is also shown that |E(POn)|=en 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.