Mathematics Problem Archive
Showing 1-7 of 7 problems
10 Lectures and 42 Open Problems — Open Problem 3.3
v1.3 research notesLet ${G=(V,E,W)}$ be a graph and ${k}$ a positive integer, is the following true? $\rho_G(k) \leq \mathrm{polylog}(k) \sqrt{\lambda_k}. \ \ \ \ \ (2)$...
10 Lectures and 42 Open Problems — Deterministic Restricted Isometry Property matrices
v1.3 research notesConstruct deterministic matrices $A\in\mathbb{C}^{M\times N}$ (or $A\in\mathbb{R}^{M\times N}$ ) satisfying the $(s,\frac13)$ -RIP for $s\approx\frac{...
10 Lectures and 42 Open Problems — Mutually Unbiased Bases
v1.3 research notesHow many mutually unbiased bases are there in 6 dimensions?...
10 Lectures and 42 Open Problems — Constructive Kadison-Singer
v1.3 research notesGive a (polynomial time) construction of the tight frame partition satisfying the properties required in the Kadison-Singer problem (or the related We...
10 Lectures and 42 Open Problems — The Grothendieck Constant
v1.3 research notesWhat is the value of the (real) Grothendieck constant?...
Simple Linear-Time Polygon Triangulation
v1.3 research notesIs there a deterministic, linear-time polygon triangulation algorithm significantly simpler than that of Chazelle?...
Sorting $X+Y$ (Pairwise Sums)
v1.3 research notesGiven two sets of numbers, each of size $n$, how quickly can the set of all pairwise sums be sorted? In symbols, given two sets $X$ and $Y$, our goal ...