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math.CO2024
Words Avoiding Tangrams
Michał Dębski, Jarosław Grytczuk, Bartłomiej Pawlik +2
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 o…
math.CO2024
Neighborly boxes and bipartite coverings; constructions and conjectures
Jarosław Grytczuk, Andrzej P. Kisielewicz, Krzysztof Przesławski
Two axis-aligned boxes in are \emph{-neighborly} if their intersection has dimension at least and at most . The maximum number of pairwise -neighbor…
math.CO2024
Largest bipartite sub-matchings of a random ordered matching or a problem with socks
Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński
Let be an ordered matching of size , that is, a partition of the set into 2-element subsets. The sock number of is the maximum size of a sub-matching of in wh…