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I am looking for a straightforward way to upper bound the covering number of a $d$-dimensional euclidean ball by $\ell_\infty$-balls of radius $\varepsilon$, which I will call cubes of sidelength $2\...

Let $\|\cdot\|_2$ denote the Euclidean norm, let $\langle \cdot, \cdot\rangle$ denote the standard dot product, and let $\mathcal{S}^{d-1} = \{\mathbf{x} \in \mathbb{R}^d: \|\mathbf{x}\|_2 = 1\}$ ...

Imagine you dump congruent, hard, frictionless balls in a box, letting gravity compress the balls into a stable configuration (I believe such configurations are called jammed.) Assume the box ...

Usually disk packing problems require that no two disks of the packing intersect. Does anybody know if the problem has been studied when disks may intersect but they are not allowed to contain the ...