Multi-crossings and Petal Number for Classical and Virtual Knots

Instead of considering projections of knots with two strands crossing at every crossing, we can ask for n strands to cross at every crossing. We will show that every knot and link has such an n-crossing projection for all integers n greater than 1 and therefore an n-crossing number. We also show that every knot has a projection with a single multi-crossing and no nested loops, which is a petal projection and which generates a petal number. We will discuss these ideas for both classical and virtual knots.