The Fibonacci Numbers—Exposed More Discretely

More properties of the Fibonacci word on an infinite alphabet

Recently the Fibonacci word $W$ on an infinite alphabet was introduced by [Zhang et al., Electronic J. Combinatorics 24-2 (2017) #P2.52] as a fixed point of the morphism $\phi: (2i) \mapsto (2i)(2i+ 1),\ (2i+ 1) \mapsto (2i+ 2)$ over all $i \in \mathbb{N}$. In this paper we investigate the occurrence of squares, palindromes, and Lyndon factors in this infinite word.

More on the Fibonacci Sequence and Hessenberg Matrices

Five new classes of Fibonacci-Hessenberg matrices are introduced. Further, we introduce the notion of two-dimensional Fibonacci arrays and show that three classes of previously known Fibonacci-Hessenberg matrices and their generalizations satisfy this property. Simple systems of linear equations are given whose solutions are Fibonacci fractions.

More on Nonregular PDL: Finite Models and Fibonacci-Like Programs

We continue research on enriching propositional dynamic logic (PDL) with nonregular programs. Previous work indicates that the general problem of characterizing those extensions for which PDL becomes undecidable is probably very hard. After observing that any nonregular extension increases the expressive power of PDL, we concentrate on one-letter extensions. First, we address the issue of finit...

Is the World Evolving Discretely?

Discretely Following a Curve

Finding the similarity between paths is an important problem that comes up in many areas such as 3D modeling, GIS applications, ordering, and reachability. Given a set of points S, a polygonal curve P , and an ε > 0, the discrete set-chain matching problem is to find another polygonal curve Q such that the nodes of Q are points in S and dF (P,Q) ≤ ε. Here, dF is the discrete Fréchet distance be...