**Please note date change**
Abdullahi Umar, Khalifa University of Science and Technology, Abu Dhabi, UAE
''Some Remarks on Monoids of Contraction Mappings of a Finite Chain"
A general systematic study of the monoids/semigroups of partial contrac- tions of a finite chain and their various subsemigroups of order-preserving/order- reversing and/or order-decreasing transformations was initiated in 2013 sup- ported by a grant from The Research Council of Oman (TRC). Our aim in this talk is to present the results obtained so far by the pre- senter and his co-authors as well as others. Broadly, speaking the results can be divided into two groups: algebraic and combinatorial enumeration. The algebraic results show that these semigroups are nonregular (left) abun- dant semigroups (for n ≥ 4) whose Green’s relations admit a nontrivial characterization. The combinatorial enumeration results show links with Fibonacci numbers, Motzkin numbers and sequences some of which are in the encyclopedia of integers sequences (OEIS).
MC 5403