The trap arm is the pipe between the trap and the vent (see pic below). Most people know that code sets a maximum length for a trap-arm. This is referred to as the "trap to vent distance." However, not everybody knows that code sets a minimum length too. According to code, when the trap arm is too short it creates a crown vent.
This is based off IPC 909.3 or UPC 1002.2.
As waste discharges from a trap, flow gets turbulent immediately out of the trap (red arrow below). If you install a vent in this turbulent area, you run the risk of clogging the vent.
Remember, a clogged vent is the same as no vent... And without that vent, the trap seal can get siphoned right down the drain...rendering the trap into a useless piece of empty plastic.
To prevent creating a crown vent, simply take the diameter of the trap arm and multiply it by two.
This is the minimum trap to vent distance code allows. Anything less than this distance is a crown vent.