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We introduce some new subsemigroups of the finite full transformation semigroups T . We consider various irregular boards of different shapes and sizes to generate subsemigroups of Tnusing the four idempotent operators L, fi, U, D. These operators shift tiles on a board in four different directions (left, right, up and down) in their respective rows and columns. In this way each operator O e G —— jL, R, U, D defines a member of o the base setI = (1, 2, ... , n and the
semigroups of various properties are given as S Tp .
Imtiaz Ahmad. (2016) Single-Tile Semigroups of Shift Operators, , Proc. of the PAS: A; 53,, Issue 3.
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