Zobrazeno 1 - 10
of 185
pro vyhledávání: '"Petrov, Fedor"'
The communication matrix for two-way deterministic finite automata (2DFA) with $n$ states is defined for an automaton over a full alphabet of all $(2n+1)^n$ possible symbols: its rows and columns are indexed by strings, and the entry $(u, v)$ is $1$
Externí odkaz:
http://arxiv.org/abs/2312.05909
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
This paper classifies all modular data of integral modular fusion categories up to rank 13. Furthermore, it also classifies all integral half-Frobenius fusion rings up to rank 12. We find that each perfect integral modular fusion category up to rank
Externí odkaz:
http://arxiv.org/abs/2302.01613
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
Autor:
Cichomski, Stanisław, Petrov, Fedor
We prove a sharp upper bound for the number of high degree differences in bipartite graphs: let $ (U, V, E)$ be a bipartite graph with $U=\{u_1, u_2, \dots, u_n\}$ and $V=\{v_1, v_2, \dots, v_n\}$; for $n\ge k>\frac{n}{2}$ we show that $\sum_{1\le i,
Externí odkaz:
http://arxiv.org/abs/2204.07219
Autor:
Lovitz, Benjamin, Petrov, Fedor
Publikováno v:
Forum of Mathematics, Sigma, Volume 11, 2023, e27
Kruskal's theorem states that a sum of product tensors constitutes a unique tensor rank decomposition if the so-called k-ranks of the product tensors are large. We prove a "splitting theorem" for sets of product tensors, in which the k-rank condition
Externí odkaz:
http://arxiv.org/abs/2103.15633
Autor:
Krachun, Dmitry, Petrov, Fedor
Publikováno v:
Moscow J. Comb. Number Th. 12 (2023) 117-126
For a finite set $A\subset \mathbb{R}$ and real $\lambda$, let $A+\lambda A:=\{a+\lambda b :\, a,b\in A\}$. Combining a structural theorem of Freiman on sets with small doubling constants together with a discrete analogue of Pr\'ekopa--Leindler inequ
Externí odkaz:
http://arxiv.org/abs/2010.00119
Autor:
Gordeev, Alexey, Petrov, Fedor
Publikováno v:
Moscow J. Comb. Number Th. 10 (2021) 271-279
We provide a general framework on the coefficients of the graph polynomials of graphs which are Cartesian products. As a corollary, we prove that if $G=(V,E)$ is a graph with degrees of vertices $2d(v), v\in V$, and the graph polynomial $\prod_{(i,j)
Externí odkaz:
http://arxiv.org/abs/2007.07140
Autor:
Pak, Igor, Petrov, Fedor
We study the weighted partition function for lozenge tilings, with weights given by multivariate rational functions originally defined by Morales, Pak and Panova (2019) in the context of the factorial Schur functions. We prove that this partition fun
Externí odkaz:
http://arxiv.org/abs/2003.14236
The Alon-Tarsi number $AT(G)$ of a graph $G$ is the smallest $k$ for which there is an orientation $D$ of $G$ with max indegree $k-1$ such that the number of even and odd circulations contained in D are different. In this paper, we show that the Alon
Externí odkaz:
http://arxiv.org/abs/1912.12466