We regard a finite word u = u1u2 · · ·un up to word isomorphism as an equivalence relation on {1, 2, . . . , n} where i is equivalent to j if and only if ui = uj. Some finite words (in particular all binary words) are generated by palindromic relations of the form k ∼ j+i−k for some choice of 1 ≤ i ≤ j ≤ n and k ∈ {i, i+1, . . . , j}. That is to say, some finite words u are uniquely determined ...

We investigate the lattice of machine invariant classes [3]. This is an infinite completely distributive lattice but it is not a Boolean lattice. We show the subword complexity and the growth function create machine invariant classes. 1 Motivation In different areas of mathematics, people consider a lot of hierarchies which are typically used to classify some objects according to their complexi...

this paper studies the generalized version of thezakharov-kuznetsov benjamin-bona-mahoney equation. the functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. there are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. the results of this pape...

To any infinite word t over a finite alphabet A we can associate two infinite words min(t) and max(t) such that any prefix of min(t) (resp. max(t)) is the lexicographically smallest (resp. greatest) amongst the factors of t of the same length. We say that an infinite word t over A is fine if there exists an infinite word s such that, for any lexicographic order, min(t) = as where a = min(A). In...