Zobrazeno 1 - 10
of 456
pro vyhledávání: '"A. Grytczuk"'
Autor:
Dębski, Michał, Grytczuk, Jarosław, Pawlik, Bartłomiej, Przybyło, Jakub, Śleszyńska-Nowak, Małgorzata
A \emph{tangram} is a word in which every letter occurs an even number of times. Such word can be cut into parts that can be arranged into two identical words. The minimum number of cuts needed is called the \emph{cut number} of a tangram. For exampl
Externí odkaz:
http://arxiv.org/abs/2407.03819
Let $M$ be an ordered matching of size $n$, that is, a partition of the set $[2n]$ into 2-element subsets. The sock number of $M$ is the maximum size of a sub-matching of $M$ in which all left-ends of the edges precede all the right-ends (such matchi
Externí odkaz:
http://arxiv.org/abs/2402.02223
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
An ordered $r$-matching of size $n$ is an $r$-uniform hypergraph on a linearly ordered set of vertices, consisting of $n$ pairwise disjoint edges. Two ordered $r$-matchings are isomorphic if there is an order-preserving isomorphism between them. A pa
Externí odkaz:
http://arxiv.org/abs/2310.01394
We study decompositions of words into subwords that are in some sense similar, which means that one subword may be obtained from the other by a relatively simple transformation. Our main inspiration are shuffle squares, an intriguing class of words a
Externí odkaz:
http://arxiv.org/abs/2308.13882
Let $M_1,M_2,\ldots,M_k$ be a collection of matroids on the same ground set $E$. A coloring $c:E \rightarrow \{1,2,\ldots,k\}$ is called \emph{cooperative} if for every color $j$, the set of elements in color $j$ is independent in $M_j$. We prove tha
Externí odkaz:
http://arxiv.org/abs/2303.08776
An edge coloring of a graph $G$ is \emph{woody} if no cycle is monochromatic. The \emph{arboricity} of a graph $G$, denoted by $\arb (G)$, is the least number of colors needed for a woody coloring of $G$. A coloring of $G$ is \emph{strongly woody} if
Externí odkaz:
http://arxiv.org/abs/2303.08771
We study a new variant of \emph{connected coloring} of graphs based on the concept of \emph{strong} edge coloring (every color class forms an \emph{induced} matching). In particular, an edge-colored path is \emph{strongly proper} if its color sequenc
Externí odkaz:
http://arxiv.org/abs/2301.10578
For $r,n\ge2$, an ordered $r$-uniform matching of size $n$ is an $r$-uniform hypergraph on a linearly ordered vertex set $V$, with $|V|=rn$, consisting of $n$ pairwise disjoint edges. There are $\tfrac12\binom{2r}r$ different ways two edges may inter
Externí odkaz:
http://arxiv.org/abs/2301.02936
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