An übercrossing diagram is a knot diagram with only one crossing; such a diagram without any nested loops is called a petal projection. Every knot has a petal projection from which the knot can be recovered, but these diagrams are not in the standard double-crossing form. This paper demonstrates a manipulation of the knot into a "split" petal projection, retaining petal structure and allowing for computation of the knot determinant from petal permutations.
journal articleRanked-Choice Voting (RCV) has been proposed as a potential solution to increasing extremism in American elections. Yet there is a lack of mathematical research about the differences between RCV and the first-past-the-post primary system in place in most states. We validate the hypothesis that RCV favors moderate candidates using both proof-based methods relying on integration over high-dimensional polytopes and simulations on various simplified models. |
preprint⁴ This paper was completed with Avidit Acharya, Rohan Cherivirala, and Karsen Wahal.