11 problems

For a positive integer $r$, let $b_k(r)=\binom{k+r-1}{r}$, and let $R_n(b_k(r))$ denote the corresponding reciprocal Hankel matrix. Integrality criterion conjecture. The inverse of…

Let $F_n$ be the $n$th Fibonacci number, let $e(n,i,k)$ be the exponent used to determine the sign in the source, and let $d_k(r)$ be the Fibonomial coefficient corresponding to…

Let $\mathbf{H} \in \mathbb{R}^{n\times n}$ be a positive definite Hankel matrix with bit complexity $\ell$ and condition number bounded by $2^\ell$. An inverse symmetric positive…

Let $\mathbf{H} \in \mathbb{R}^{n\times n}$ be a positive definite Hankel matrix with bit complexity $\ell$. A symmetric positive factorization algorithm should find a representati…

Let $H=(h_{i,j})_{i,j\geq 0}$ be the Hankel matrix defined in the paper, and for $k\geq 1$ let $I=(i_1,\ldots,i_k)$ and $J=(j_1,\ldots,j_k)$ be sequences satisfying … Let $H_{I,J}$…

Strong coefficientwise Hankel-total positivity conjecture for the GKP recurrence. The sequence

Coefficientwise Hankel-total positivity conjecture for the GKP recurrence. The sequence

Let $\mathcal H_m$ be the fully generic $m\times m$ Hankel matrix, let $J=J_m[0]$ be its gradient ideal, and let $x_{m+3},\ldots,x_{2m-1}$ be the indicated variables. Regular-seque…

Let $R$ be the polynomial ring containing the entries of the generic $m\times m$ Hankel matrix $\mathcal{H}_m$. Hankel non-homaloidality conjecture. The determinant of…

Let $R$ be the polynomial ring containing the entries of the generic $m\times m$ Hankel matrix $\mathcal{H}_m$, and let $J$ be the gradient ideal of its determinant. Linear-type co…

Let $k$ be the base field, let $R$ be the polynomial ring containing the entries of the generic $m\times m$ Hankel matrix $\mathcal{H}_m$, and let $J$ be the gradient ideal of…