7 problems

Let $[K]$ be a knot class represented by lattice knots, and let $dV[K]$ denote its vertex distortion, defined as the infimum of $dV(K)$ over all lattice-knot conformations represen…

For a knot type $K$, let $n_{\operatorname{SC}}(K)$ denote its simple cubic birth level, and let $G_{n_{\operatorname{SC}}(K)}^{\operatorname{SC},\operatorname{BFACF}}(K)$ be the c…

Let $K$ be an amphichiral knot type and let $\omega$ be a minimal simple cubic lattice representative of $K$. Consider the minimal BFACF graph and the reflected mirror seed of…

Let $[K]$ be a knot type, let $s_{sh}[K]$ denote its stick number in the simple hexagonal lattice, and let $c[K]$ denote its crossing number. Crossing-number bound conjecture. For…

Let $[K]$ be a knot type, let $s_{sh}[K]$ denote its stick number in the simple hexagonal lattice, and let $3_1$, $4_1$, $5_1$, and $5_2$ denote the indicated knot types. 13-stick…

Let $T_{p,q}$ be the $(p,q)$-torus knot, let $[T_{p,q}]$ denote its lattice-knot equivalence class, and let $delta_V$ denote vertex distortion. Unbounded distortion conjecture. … T…

Lattice stick number bound. It is conjectured that