The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence
Tóm tắt
A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup
$$\mathscr {TF}_{n}$$
of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of
$$\mathscr {TF}_{n}$$
and provide a minimal generating set for
$$ \mathscr {TF}_{n}$$
. Moreover, a formula for the number of idempotents in
$$\mathscr {TF}_{n}$$
is given.
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