Verifying Fox's Conjecture for a Family of Knots:
We verify Fox's Trapezoidal Conjecture on the Alexander Polynomial for a family of alternating pretzel knots, and we extend the conjecture by verifying it for a family of quasi-alternating knots.
This was joint with Audrick Pyronneau (University of Texas at Austin) at the Topology REU at the University of Alabama. View a poster of our work here.Â
Pages 10-23 of my notes contain a full proof for the family of pretzel knots.