split petal projections⁵

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.

the theory of ranked-choice voting⁶

ranked-choice voting (rcv) has been proposed as a potential solution to increasing extremism in american election. however, 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. in this paper, 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.