42 citations · 109 across the 37 of their papers we have counts for
9 papers · 1 filter
On weak twins and up-and-down sub-permutations
Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński
Two permutations and are weakly similar if if and only if for all . Let be a permutati…
Graph Polynomials and Group Coloring of Graphs
Bartłomiej Bosek, Jarosław Grytczuk, Grzegorz Gutowski +2
Let be an Abelian group and let be a simple graph. We say that is -colorable if for some fixed orientation of and every edge labeling , t…
Square-free reducts of words
Jarosław Grytczuk, Szymon Stankiewicz
A \emph{square} is a finite non-empty word consisting of two identical adjacent blocks. A word is \emph{square-free} if it does not contain a square as a factor. In any finite word…
Reflections on the Erd\H {o}s Discrepancy Problem
Bartłomiej Bosek, Jarosław Grytczuk
We consider some coloring issues related to the famous Erd\H {o}s Discrepancy Problem. A set of the form , with , is called a \emph{ho…
Dilworth's Theorem for Borel Posets
Bartłomiej Bosek, Jarosław Grytczuk, Zbigniew Lonc
A famous theorem of Dilworth asserts that any finite poset of width can be decomposed into chains. We study the following problem: given a Borel poset of finite width $…
Graph polynomials and paintability of plane graphs
Jarosław Grytczuk, Stanislav Jendrol', Mariusz Zając
There exists a variety of coloring problems for plane graphs, involving vertices, edges, and faces in all possible combinations. For instance, in the \emph{entire coloring} of a pl…
From the 1-2-3 Conjecture to the Riemann Hypothesis
Jarosław Grytczuk
This survey presents some combinatorial problems with number-theoretic flavor. Our journey starts from a simple graph coloring question, but at some point gets close to a dangerous…
Majority choosability of countable graphs
Marcin Anholcer, Bartłomiej Bosek, Jarosław Grytczuk
In any vertex coloring of a graph some edges have differently colored ends (\emph{good} edges) and some are monochromatic (\emph{bad} edges). In a proper coloring all edges are goo…
Variations on twins in permutations
Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński
Let be a permutation of the set . Two disjoint order-isomorphic subsequences of are called twins. How long twins are contained in every permutation? T…