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pro vyhledávání: '"Kisielewicz, Andrzej P."'
Two axis-aligned boxes in $\mathbb{R}^d$ are \emph{$k$-neighborly} if their intersection has dimension at least $d-k$ and at most $d-1$. The maximum number of pairwise $k$-neighborly boxes in $\mathbb{R}^d$ is denoted by $n(k,d)$. It is known that $n
Externí odkaz:
http://arxiv.org/abs/2402.02199
Autor:
Kisielewicz, Andrzej P.
Let $n,d\in \mathbb{N}$ and $n>d$. An $(n-d)$-domino is a box $I_1\times \cdots \times I_n$ such that $I_j\in \{[0,1],[1,2]\}$ for all $j\in N\subset [n]$ with $|N|=d$ and $I_i=[0,2]$ for every $i\in [n]\setminus N$. If $A$ and $B$ are two $(n-d)$-do
Externí odkaz:
http://arxiv.org/abs/2401.00759
Autor:
Kisielewicz, Andrzej P.
Two $d$-dimensional simplices in $R^d$ are neighborly if its intersection is a $(d-1)$-dimensional set. A family of $d$-dimensional simplices in $R^d$ is called neighborly if every two simplices of the family are neighborly. Let $S_d$ be the maximal
Externí odkaz:
http://arxiv.org/abs/2310.19965
A family of axis-aligned boxes in $\er^d$ is \emph{$k$-neighborly} if the intersection of every two of them has dimension at least $d-k$ and at most $d-1$. Let $n(k,d)$ denote the maximum size of such a family. It is known that $n(k,d)$ can be equiva
Externí odkaz:
http://arxiv.org/abs/2212.05133
Autor:
Grech, Mariusz, Kisielewicz, Andrzej
The distinguishing index $D'(\Gamma)$ of a graph $\Gamma$ is the least number $k$ such that $\Gamma$ has an edge-coloring with $k$ colors preserved only by the trivial automorphism. In this paper we prove that if the automorphism group of a finite gr
Externí odkaz:
http://arxiv.org/abs/2107.09452
Autor:
Grech, Mariusz, Kisielewicz, Andrzej
An edge-coloring of a graph is called asymmetric if the only automorphism which preserves it is the identity. Lehner, Pil\'{s}niak, and Stawiski proved that all connected regular graphs except $K_2$ admit an asymmetric edge-coloring with three colors
Externí odkaz:
http://arxiv.org/abs/2107.09449
Autor:
Grech, Mariusz, Kisielewicz, Andrzej
The distinguishing number $D(G,X)$ of an action of a group $G$ on a set $X$ is the least size of a partition of $X$ such that no element of $G$ acting nontrivially on $X$ preserves this partition. In this paper we describe the distinguishing numbers
Externí odkaz:
http://arxiv.org/abs/2009.09275
Autor:
Kisielewicz, Andrzej P.
Let $S$ be a set of arbitrary objects, and let $s\mapsto s'$ be a permutation of $S$ such that $s"=(s')'=s$ and $s'\neq s$. Let $S^d=\{v_1...v_d\colon v_i\in S\}$. Two words $v,w\in S^d$ are dichotomous if $v_i=w'_i$ for some $i\in [d]$, and they for
Externí odkaz:
http://arxiv.org/abs/2008.10016
Autor:
Grech, Mariusz, Kisielewicz, Andrzej
The distinguishing number $D(\Gamma)$ of a graph $\Gamma$ is the least size of a partition of the vertices of $\Gamma$ such that no non-trivial automorphism of $\Gamma$ preserves this partition. We show that if the automorphism group of a graph $\Gam
Externí odkaz:
http://arxiv.org/abs/2001.06300
We prove a combinatorial theorem on families of disjoint sub-boxes of a discrete cube, which implies that there are at most $2^{d+1}-2$ nearly neighbourly simplices in $\mathbb R^d$.
Comment: 6 pages, accepted to Discrete Comput. Geom
Comment: 6 pages, accepted to Discrete Comput. Geom
Externí odkaz:
http://arxiv.org/abs/1912.13176