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