A word u defined over an alphabet A is c-balanced (c ∈ N) if for all pairs of factors v, w of u of the same length and for all letters a ∈ A, the difference between the number of letters a in v and w… (More)

The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints… (More)

We consider boundary conditions at the vertex of a star graph which make Schrödinger operators on the graph self-adjoint, in particular, the two-parameter family of such conditions invariant with… (More)

We study Schrödinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by δ-couplings with a parameter α ∈ R. If the graph is… (More)

According to a result of Richomme, Saari and Zamboni, the abelian complexity of the Tribonacci word satisfies ρ(n) ∈ {3, 4, 5, 6, 7} for each n ∈ N. In this paper we derive a formula for evaluating… (More)

The m-bonacci word is a generalization of the Fibonacci word to the m-letter alphabet A = {0, . . . ,m − 1}. It is the unique fixed point of the Pisot–type substitution φm : 0 → 01, 1 → 02, . . . ,… (More)

The paper is concerned with the number of open gaps in spectra of periodic quantum graphs. The well-known conjecture by Bethe and Sommerfeld (1933) says that the number of open spectral gaps for a… (More)