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Divergent permutations
Emanuela Fachini, János Körner
Two permutations of the natural numbers diverge if the absolute value of the difference of their elements in the same position goes to infinity. We show that there exists an infini…
Interlocked permutations
Gerard Cohen, Emanuela Fachini, Janos Korner
The zero-error capacity of channels with a countably infinite input alphabet formally generalises Shannon's classical problem about the capacity of discrete memoryless channels. We…
Hamilton paths with lasting separation
Janos Korner, Emanuela Fachini
We determine the asymptotics of the largest cardinality of a set of Hamilton paths in the complete graph with vertex set [n] under the condition that for any two of the paths in th…
Path separation by short cycles
Gérard Cohen, Emanuela Fachini, János Körner
Two Hamilton paths in are separated by a cycle of length if their union contains such a cycle. For small fixed values of we bound the asymptotics of the maximum cardi…
Zero-error capacity of binary channels with memory
Gérard Cohen, Emanuela Fachini, János Körner
We begin a systematic study of the problem of the zero--error capacity of noisy binary channels with memory and solve some of the non--trivial cases.
Skewincidence
Gerard Cohen, Emanuela Fachini, Janos Korner
We introduce a new class of problems lying halfway between questions about graph capacity and intersection. We say that two binary sequences x and y of the same length have a skewi…