It has been shown that the twist number of a reduced alternating knot can be determined by summing certain coefficients in the Jones Polynomial. In the discovery of this twist number, it became evident that there exist higher order twist numbers which are the sums of other coefficients. Some relations between the second twist number and the first are explored while noting special characteristics of the second twist number.
"On the Second Twist Number,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 7:
1, Article 6.
Available at: https://scholar.rose-hulman.edu/rhumj/vol7/iss1/6