Combinatorial results for semigroups of order-preserving partial transformations

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 c 0 = 1, c 1 = 2. It is also shown that |E(PO n )| = e n satisfies the recurrence e n+1 = 5(e n − e n−1 ) + 1 with initial conditions e 0 = 1, e 1 = 2. Moreover, the cardinalities of the Green's relations L, R and J have been computed.

On semigroups of order-preserving transformations of countable linearly ordered sets

“…For i = 1, the statement of the lemma follows from (3). Assume that the lemma has already been proved for i < m. Let us prove it for m. Then either m ≤ s 0 and, using inequality (3), we get …”

“…The semigroup properties of these semigroups (existence of idempotents, regularity, cancellation, and residual finiteness) are considered in Sec. 3. The Green relations are described in Sec.…”

Dissipative Properties of ω-Order Preserving Partial Contraction Mapping in Semigroup of Linear Operator

“…Batty [7] obtained asymptotic behaviour of semigroup of operator in Banach space. More relevant work and results on dissipative properties of ω-Order preserving partial contraction mapping in semigroup of linear operator could be seen in Engel and Nagel [8], Vrabie [9], Laradji and Umar [10], Rauf and Akinyele [11] and Rauf et al [12].…”

Polarity in signed symmetric group and signed transformation semigroup

“…The study of symmetric groups, alternating groups and dihedral groups has made a significant contribution to group theory, so has the study of various subsemigroups of , and (Bashar 2010;Howie 2002;Laradji and Umar 2004;Umar 1992). Extensive research work have been done in the area of semigroup see Higgins 1992), (Laradji and Umar 2004), (Adeniji2012), (Adeshola2013). (Bakare and Makanjuola 2013), (Mogbonju2015).…”