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.

Author Bio

My name is Gabriel Murillo and I am a mathematics undergraduate at UC Riverside. From July 5 㤼㸶 August 26, 2005, I participated in an NSF funded Research Experience for Undergraduates (REU) program at California State University, San Bernardino. During this REU I worked under my sponsor, Mathematician Dr. Rolland Trapp, and completed a Knot Theory research paper entitled "On the Second Twist Number."