In this paper we consider the avoidance of patterns in infinite words. Generalising the traditional problem setting, functional dependencies between pattern variables are allowed here, in particular, patterns involving permutations. One of the remarkable facts is that in this setting the notion of avoidability index (the smallest alphabet size for which a pattern is avoidable) is meaningless si...

A graphG = (V,E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if xy is an edge in E. Word-representable graphs are the main focus in “Words and Graphs” by Kitaev and Lozin. A word w = w1 · · ·wn avoids the pattern 132 if there are no 1 ≤ i1 < i2 < i3 ≤ n such that wi1 < wi3 < wi2. A recently suggested research direction ...

In the debate on how we ought to define political freedom, some definitions are criticized for implying that no one can ever be free perform any action. this paper, I show possibility of freedom depends a definition finds an appropriate balance between absence interference and protection against interference. To assess different conceptions consider trade-offs they make these two dimensions. fi...

We find all finite unavoidable ordered sets, finite unavoidable semilattices and finite unavoidable lattices.