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4 papers
A multi-plank generalization of the Bang and Kadets inequalities
Alexey Balitskiy
If a convex body is covered by the union of convex bodies , multiple subadditivity questions can be asked. Two classical results regard t…
Flip cycles in plabic graphs
Alexey Balitskiy, Julian Wellman
Planar bicolored (plabic) graphs are combinatorial objects introduced by Postnikov to give parameterizations of the positroid cells of the totally nonnegative Grassmannian $\text{G…
Optimality of codes with respect to error probability in Gaussian noise
Alexey Balitskiy, Roman Karasev, Alexander Tsigler
We consider geometrical optimization problems related to optimizing the error probability in the presence of a Gaussian noise. One famous questions in the field is the "weak simple…
Dependence of the heavily covered point on parameters
Alexey Balitskiy, Roman Karasev
We examine Gromov's method of selecting a point "heavily covered" by simplices formed by a given finite point sets, in order to understand the dependence of the heavily covered poi…