3 citations · 7 across the 34 of their papers we have counts for
5 papers · 1 filter
The kissing number in 48 dimensions for codes with certain forbidden distances is 52 416 000
Peter Boyvalenkov, Danila Cherkashin
We prove that the kissing number in 48 dimensions among antipodal spherical codes with certain forbidden inner products is 52\,416\,000. Constructions of attaining codes as kissing…
On stability of weighted spanning tree degree enumerators
Danila Cherkashin, Pavel Prozorov
Our previous paper shows that the (vertex) spanning tree degree enumerator polynomial of a connected graph is a real stable polynomial (id est is non-zero if all variables have…
Branching points in the planar Gilbert--Steiner problem have degree 3
Danila Cherkashin, Fedor Petrov
Gilbert--Steiner problem is a generalization of the Steiner tree problem on a specific optimal mass transportation. We show that every branching point in a solution of the planar G…
On small non-uniform hypergraphs without property B
Danila Cherkashin
For a given hypergraph consider the sum of over . Consider the class of hypergraphs with the smallest edge of size and without a 2-colour…
A self-similar infinite binary tree is a solution of Steiner problem
D. Cherkashin, Y. Teplitskaya
We consider a general metric Steiner problem which is of finding a set with minimal length such that is connected, where is a given compact s…