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pro vyhledávání: '"Filakovský, Marek"'
Aougab and Gaster [Math. Proc. Cambridge Philos. Soc. 174 (2023), 569--584] proved that any set of simple closed curves on the torus, where any two are non-homotopic and intersect at most $k$ times, has a maximum size of $k+O(\sqrt{k}\log k)$. We pro
Externí odkaz:
http://arxiv.org/abs/2412.18002
A linearly ordered (LO) $k$-colouring of a hypergraph is a colouring of its vertices with colours $1, \dots, k$ such that each edge contains a unique maximal colour. Deciding whether an input hypergraph admits LO $k$-colouring with a fixed number of
Externí odkaz:
http://arxiv.org/abs/2312.12981
Autor:
Filakovský, Marek, Vokřínek, Lukáš
We present an algorithm that, given finite simplicial sets $X$, $A$, $Y$ with an action of a finite group $G$, computes the set $[X,Y]^A_G$ of homotopy classes of equivariant maps $\ell \colon X \to Y$ extending a given equivariant map $f \colon A \t
Externí odkaz:
http://arxiv.org/abs/2104.10152
A central problem of algebraic topology is to understand the homotopy groups $\pi_d(X)$ of a topological space $X$. For the computational version of the problem, it is well known that there is no algorithm to decide whether the fundamental group $\pi
Externí odkaz:
http://arxiv.org/abs/1706.00380
Autor:
Filakovský, Marek
Publikováno v:
Archivum Mathematicum 050.5 (2014): 273-286
We extend the notion of simplicial set with effective homology to diagrams of simplicial sets. Further, for a given finite diagram of simplicial sets $X \colon \mathcal{I} \to \mathsf{sSet}$ such that each simplicial set $X(i)$ has effective homology
Externí odkaz:
http://arxiv.org/abs/1410.3396
Autor:
Filakovský, Marek, Vokřínek, Lukáš
This paper presents two algorithms. In their simplest form, the first algorithm decides the existence of a pointed homotopy between given simplicial maps f, g from X to Y and the second computes the group $[\Sigma X,Y]^*$ of pointed homotopy classes
Externí odkaz:
http://arxiv.org/abs/1312.2337
Autor:
Filakovský, Marek
Publikováno v:
Archivum Mathematicum 048.5 (2012): 313-322
In the paper weak sufficient conditions for the reduction of the chain complex of a twisted product to a free finitely generated chain complex are found.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/1209.1240
Akademický článek
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Publikováno v:
Journal of Applied & Computational Topology; Dec2018, Vol. 2 Issue 3/4, p177-231, 55p
