4 problems

Standard-Vandermonde determinant formula. The first appearance value is

Standard-Vandermonde value conjecture. For $n \geq 2$,

Let $X=\{x_0=1,x_1,\ldots,x_k\}$ be a set of pairwise distinct roots of unity, and let $B=\{b_0=0,b_1,\ldots,b_m\}$ be a set of coprime integer numbers. Let $M=(x_i^{b_j})$ be dege…

Let $b>1$, and set … For each $n$, let $M_b(n)$ denote the largest absolute value of an entry of the inverse Vandermonde matrix, and let $c_{i,j,n}$ denote its entries. Diagonal-ma…