9 problems

Asymptotic separation conjecture. For every probability vector $(p,1-p)$, there exists a positive integer $N$ such that, for all $n eg N$, the optimal set $alphan$ contains points…

Let $n$ be a positive integer, and let the Zador upper bound be the upper bound on normalized second moment for arbitrary quantizers in dimension $n$. Lattice-quantizer attainment…

Let $x$ be a real number and define the probability vector $(p_1,p_2,p_3,\ldots)$ by … For each positive integer $n$, let $\alpha_n$ denote the proposed set of $n$-means, and let…

Let $m\geq 3$, let $x$ be a real number, and define the probability vector $(p_1,p_2,\ldots,p_m)$ by … For each $n$, let $\alpha_n$ denote the proposed set of $n$-means, and let…

Pena et al.'s conjecture. The quantization coefficient for the uniform distribution on the boundary of a regular $m$-sided polygon inscribed in a circle is an increasing function o…

Roychowdhury's conjecture. The Voronoi regions of the points in an optimal set of two-means partition the disc into two semicircles.

Nonexistence conjecture. Unlike in the homogeneous case, a closed formula cannot be obtained for the optimal sets of $n$-means for the nonhomogeneous probability distribution consi…

Let $s_r$ be the unique solution of … For the self-affine measure $\mu$ on the Bedford–McMullen carpet $E$, consider the two conditions: (a)…

Gersho's conjecture. As $N$ tends to infinity, most cells—namely, all cells except those close to the boundary of the considered domain—become congruent to $H_d^*$.