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Combinatorics of Dyadic Intervals: Consistent Colourings

Anna Kamont, Paul F. X. Müller (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

We study the problem of consistent and homogeneous colourings for increasing families of dyadic intervals. We determine when this problem can be solved and when it cannot.

Completely dissociative groupoids

Milton Braitt, David Hobby, Donald Silberger (2012)

Mathematica Bohemica

In a groupoid, consider arbitrarily parenthesized expressions on the k variables x 0 , x 1 , x k - 1 where each x i appears once and all variables appear in order of their indices. We call these expressions k -ary formal products, and denote the set containing all of them by F σ ( k ) . If u , v F σ ( k ) are distinct, the statement that u and v are equal for all values of x 0 , x 1 , x k - 1 is a generalized associative law. Among other results, we show that many small groupoids are completely dissociative, meaning that no generalized associative law holds...

Complexité et automates cellulaires linéaires

Valérie Berthé (2010)

RAIRO - Theoretical Informatics and Applications

The aim of this paper is to evaluate the growth order of the complexity function (in rectangles) for two-dimensional sequences generated by a linear cellular automaton with coefficients in / l , and polynomial initial condition. We prove that the complexity function is quadratic when l is a prime and that it increases with respect to the number of distinct prime factors of l.

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