5 problems

Let a free knot diagram be given, and let a nontrivial knot be a knot other than the unknot. The resultant knot probability is the proportion of crossing assignments of the free kn…

A free tangle is a tangle whose crossings are free crossings, and its four anchor points remain fixed on the boundary. The resultant knot probability is the proportion of crossing…

Let $K_1$ be a nontrivial prime knot with resultant unknot probability $\alpha$, and let $K_2$ be a nontrivial prime knot formed by recursive connected sums with $K_1$. Write…

A free $2n$ knot is the free knot diagram referred to in the source, with $n+2$ crossings. A minimal free knot diagram is one with the minimum crossing number for its knot. $2n$-un…

A resultant knot probability is the proportion of crossing assignments of a free knot diagram that produce a specified knot. An algebraic tangle is a tangle obtained through the al…