Rectangle condition on $n$-bridge presentation of knots

In this paper, we define the rectangle condition for $n$-bridge presentation of knots whose definition is analogous to the definition of the rectangle condition for Heegaard splittings of $3$-manifolds. We show that the satisfaction of the rectangle condition for $n$-bridge presentation can guarantee that the Hempel distance for the $n$-bridge presentation is greater than or equal to $2$. Especially, we find a certain condition of $6$-plat presentations to be alternating $3$-bridge knots by using the rectangle condition.