We first show that the three-variable bracket polynomial is an invariant for reduced, alternating links. We then try to find what the polynomial reveals about knots. We find that the polynomial gives the crossing number, a test for chirality, and in some cases, the twist number of a knot. The extreme degrees of d are also studied.
Prof. Rolland Trapp, Department of Mathematics, California State University, San Bernardino
"The Three-Variable Bracket Polynomial for Reduced, Alternating Links,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 14
, Article 7.
Available at: http://scholar.rose-hulman.edu/rhumj/vol14/iss2/7