Zobrazeno 1 - 10
of 87
pro vyhledávání: '"Cherkashin, Danila"'
Autor:
Cherkashin, Danila
Consider a family $\mathcal{F}$ of $k$-subsets of an ambient $(k^2-k+1)$-set such that no pair of $k$-subsets in $\mathcal{F}$ intersects in exactly one element. In this short note we show that the maximal size of such $\mathcal{F}$ is $\binom{k^2-k-
Externí odkaz:
http://arxiv.org/abs/2408.00484
The Euclidean Steiner problem is the problem of finding a set $St$, with the shortest length, such that $St \cup A$ is connected, where $A$ is a given set in a Euclidean space. The solutions $St$ to the Steiner problem will be called Steiner sets whi
Externí odkaz:
http://arxiv.org/abs/2404.11546
Autor:
Boyvalenkov, Peter, Cherkashin, Danila
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 configurations of minimum vectors in even unimodular extremal lattice
Externí odkaz:
http://arxiv.org/abs/2312.05121
Autor:
Cherkashin, Danila, Prozorov, Pavel
Our previous paper shows that the (vertex) spanning tree degree enumerator polynomial of a connected graph $G$ is a real stable polynomial (id est is non-zero if all variables have positive imaginary parts) if and only if $G$ is distance-hereditary.
Externí odkaz:
http://arxiv.org/abs/2310.18051
Autor:
Cherkashin, Danila, Petrov, Fedor
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 Gilbert--Steiner problem has degree 3.
Externí odkaz:
http://arxiv.org/abs/2309.04202
Autor:
Cherkashin, Danila
For a given hypergraph $H = (V,E)$ consider the sum $q(H)$ of $2^{-|e|}$ over $e \in E$. Consider the class of hypergraphs with the smallest edge of size $n$ and without a 2-colouring without monochromatic edges. Let $q(n)$ be the smallest value of $
Externí odkaz:
http://arxiv.org/abs/2303.03803
Autor:
Cherkashin, Danila, Teplitskaya, Yana
Consider a compact $M \subset \mathbb{R}^d$ and $l > 0$. A maximal distance minimizer problem is to find a connected compact set $\Sigma$ of the length (one-dimensional Hausdorff measure $\mathcal H$) at most $l$ that minimizes \[ \max_{y \in M} dist
Externí odkaz:
http://arxiv.org/abs/2212.05607
Consider a compact $M \subset \mathbb{R}^d$ and $r > 0$. A maximal distance minimizer problem is to find a connected compact set $\Sigma$ of the minimal length, such that \[ \max_{y \in M} dist (y, \Sigma) \leq r. \] The inverse problem is to determi
Externí odkaz:
http://arxiv.org/abs/2212.01903
We show that the spanning tree degree enumerator polynomial of a connected graph $G$ is a real stable polynomial if and only if $G$ is distance-hereditary.
Externí odkaz:
http://arxiv.org/abs/2209.04413
This paper deals with the minimum number $m_H(r)$ of edges in an $H$-free graph with the chromatic number more than $r$. We show how bounds on Ramsey and Tur\'an numbers imply bounds on $m_H(r)$.
Externí odkaz:
http://arxiv.org/abs/2207.05840