4 papers · 1 filter
A Quantitative Helly-type Theorem: Containment in a Homothet
Grigory Ivanov, Márton Naszódi
We introduce a new variant of quantitative Helly-type theorems: the minimal \emph{"homothetic distance"} of the intersection of a family of convex sets to the intersection of a sub…
On the volume of sections of the cube
Grigory Ivanov, Igor Tsiutsiurupa
We study the properties of the maximal volume -dimensional sections of the -dimensional cube . We obtain a first order necessary condition for a -dimensional sub…
Orthodiagonal anti-involutive Kokotsakis polyhedra
Ivan Erofeev, Grigory Ivanov
We study the properties of Kokotsakis polyhedra of orthodiagonal anti-involutive type. Stachel conjectured that a certain resultant connected to a polynomial system describing flex…
On the volume of projections of the cross-polytope
G. Ivanov
We study properties of the volume of projections of the -dimensional cross-polytope $\crosp^n = \{ x \in \R^n \mid |x_1| + \dots + |x_n| \leqslant 1\}.$ We prove that the projec…