9 problems

Let $K$ be a knotoid diagram. Let $K_1$ and $K_2$ be the starred knotoid diagrams obtained from $K$ by placing a star in the region incident to the tail and the region incident to…

Topological specialization conjecture. The two mock Alexander polynomials satisfy

Star-placement symmetry conjecture. The potentials satisfy

Minimum-volume conjecture. The unique spherical knotoid of smallest volume is the knotoid $2_1$, and its volume is approximately $5.33349\dots$.

Let $D$ be a linear chord diagram with one chord for a planar knotoid, and write its corresponding word as $c=a^{n_1}b^{m_1}\dots a^{n_k}b^{m_k}$, where $k<\infty$ and…

Let $K$ be a virtual knot of genus one, and let a torus representation be a representation of $K$ by a knot diagram in the thickened torus. The surface bracket states of such a rep…

Let $s\kappa_n$ be the number of $n$-crossing knotoid diagrams, let $sk_n$ be the number of $n$-crossing knotoid shadows, and let $\mu_K$ be the knotoid-shadow connective constant.…

Let $sk_n$ be the number of $n$-crossing knotoid shadows, let $\mu_I$ be the connective constant for knot shadows, and let $\mu_K$ be the connective constant for knotoid shadows. E…

Classical knotoid embedding conjecture. If two knotoid diagrams in $S^2$ are virtually equivalent, then they are equivalent to each other by finitely many $\Omega$-moves and isotop…