Abstract
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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