187 citations · 232 across the 22 of their papers we have counts for
4 papers · 1 filter
The sign-sequence constant of the plane
Ben Lund, Alexander Magazinov
Let be a finite-dimensional real normed space, and let be the unit ball in . The sign sequence constant of is the least such that, for each sequence $v_1, \ldo…
On Delaunay's classification theorem on faces of parallelohedra of codimension three
Alexander Magazinov
In 1929 B.~N.~Delaunay proved that there are exactly 5 types of coincidence of parallelohedra at faces of codimension 3. We give a combinatorial proof of this theorem and prove sev…
Fair partitioning by straight lines
Augustin Fruchard, Alexander Magazinov
A pizza is a pair of planar convex bodies ,where represents the dough and the topping of the pizza. A partition of a pizza by straight lines is a succession o…
Positive-fraction intersection results and variations of weak epsilon-nets
Alexander Magazinov, Pablo Soberón
Given a finite set of points in and a family of sets generated by the pairs of points of , we determine volumetric and structural conditions for the sets that allo…