20 problems

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…

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 $F_n$ denote the $n$th Fibonacci number. A Fibonomial coefficient is obtained by replacing the binomial coefficients in the corresponding reciprocal Hankel matrices with Fibono…

Let $M_N(\phi)$ denote the symmetric Toeplitz + Hankel matrix associated with the generating function $\phi$, and let $t_{\beta,\theta}$ denote the singularity factor used in the p…

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 $m$ be the matrix size, let $\J_m[r]$ denote the gradient ideal associated with the coordinate section $\mathcal H_m[r]$, and assume the ground characteristic is zero. Linear-r…

Let ${\mathbf A}\in\mathbb{C}^{M\times N}$, and consider the Cadzow algorithm for rank-1 Hankel approximation. The algorithm's fixed point is compared with an optimal rank-1 Hankel…

Hankel rank conjecture. Then

Let $H_N$ be the $N\times N$ Hankel moment matrix generated by the weight $w(x)={\rm e}^{-x^{\beta}}$ on $[0,\infty)$, with $\beta>0$, and let $\lambda_{\min}(H_N)$ denote its smal…

Let $x_1,x_2,\dots,x_n$ be pairwise distinct numbers and let $\omega_1,\dots,\omega_n$ be nonzero. Consider the linear functional … For each $k$, let $H_k$ be the associated Hankel…

Let d53d_{dd denote the sequence of Hankel determinants defined in the paper, and let $m$ be a nonnegative integer and $j$ be odd. BellHareAmdeberhanMoll conjecture. The recursiv…

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…

Let $A\in\mathbb{C}^{n\times n}$ be a complex square matrix. A Toeplitz matrix is a matrix constant along each diagonal, and a Hankel matrix is a matrix constant along each antidia…

Let $(s_n)$ be the moment sequence of a positive measure on $[0,∞)$ with density $e^{-t^{\beta}}$ with respect to Lebesgue measure, and let $\lambda_N$ denote the smallest eigenval…