8 problems

Let $L$ be a link and let $\mathrm{top}(L,q)$ denote the top coefficient of its Links-Gould invariant. A Murasugi sum is the surface operation described in the paper, and let the a…

2d log-concavity conjecture. The absolute values $(|a_{ij}|)$ form a 2d log-concave sequence with no interior zeros. This conjecture is proposed as a bidimensional analogue of log-…

Strong version of Ishii's conjecture. The coefficients satisfy $a_{ij}=(-1)^{\mu+i+j+1}|a_{ij}|$ for all $i,j$, and $(a_{ij})$ has no interior zeros. The source notes that this str…

Ishii's conjecture. The polynomial is alternating: $a_{ij}a_{i'j'}\geq 0$ if $i+j-i'-j'$ is even, and $a_{ij}a_{i'j'}\leq 0$ otherwise. Ishii verified the conjecture for all prime…

Let $K$ be a positive knot, and let $\mathrm{top}(K,q)$ denote the top coefficient of its Links-Gould invariant. A positive integer combination of positive powers of $q$ is a polyn…

Let $ADO_3$ denote the single-colored $ADO_3$ invariant of links, and let $LG$ denote the Links-Gould polynomial. A specialization of $LG$ is called well chosen if it recovers the…

Let $b1\in\mathbb{C}\setminus\mathbb{Q}$, let $H_n(\alpha)$ be the cubic Hecke algebra through which the braid-group representation factors, and let $r_2$ and $r_3$ be the relation…

Fix $b1 enewcommand$?