Semigroup Theory and Algebra

Enumeration of certain semigroups of transformations

Dr. Abdullahi Umar

  • Enumerative problems of an essentially combinatorial nature arise naturally in the study of semigroups of transformations. Amongst other things, enumerating the sizes of various equivalence classes on semigroups of transformations is our main objective in this project.


Studies in semigroups of contraction mappings of a finite chain

Dr. Abdullahi Umar (co-PI)

  • A general systematic study of the semigroups of partial contraction mappings of a finite chain and their various subsemigroups of order-preserving/reversing and/or order-decreasing transformations is undertaken in this project.


Magic squares and cubes                

Dr. Abdullahi Umar

  • New construction methods of magic squares and cubes are explored in this project.