The Rank of the Trip Matrix of a Positive Knot Diagram

In this note we show that the rank of the trip matrix of a positive knot diagram is exactly twice the genus of the associated positive knot. From this, we give a quick proof of the following result of Murasugi: The term of lowest degree in the Jones polynomial of a positive knot is 1 · t^g, where g is the genus of the knot.