Department of Mathematics Seminar: Abdullahi Umar, Khalifa University, Abu Dhabi, UAE (Monday, July 29, 2019)

Speaker

Abdullahi Umar, Department of Mathematics, Petroleum Institute, Khalifa University, Abu Dhabi, UAE

Title

Some Remarks on Monoids of Contraction Mappings of a Finite Chain

Abstract

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).

Date

Monday, July 29, 2019

Time

4 p.m. - 4:50 p.m.

Location

LH3058 (Lazaridis Hall, Room 3058)