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Abdullahi Umar, Department of Mathematics, Petroleum Institute, Khalifa University, Abu Dhabi, UAE
Some Remarks on Monoids of Contraction Mappings of a Finite Chain
A general systematic study of the monoids/semigroups of partial contractions of a finite chain and their various subsemigroups of order-preserving/order-reversing and/or order-decreasing transformations, supported by a grant from The Research Council of Oman (TRC), was initiated in 2013. Our aim in this talk is to present the results obtained so far by the presenter 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) abundant 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).
Monday, July 29, 2019
4 p.m. - 4:50 p.m.
LH3058 (Lazaridis Hall, Room 3058)