Rich and Periodic-Like Words
نویسندگان
چکیده
In this paper we investigate the periodic structure of rich words (i.e., words having the highest possible number of palindromic factors), giving new results relating them with periodic-like words. In particular, some new characterizations of rich words and rich palindromes are given. We also prove that a periodic-like word is rich if and only if the square of its fractional root is also rich.
منابع مشابه
A particle swarm optimization method for periodic vehicle routing problem with pickup and delivery in transportation
In this article, multiple-product PVRP with pickup and delivery that is used widely in goods distribution or other service companies, especially by railways, was introduced. A mathematical formulation was provided for this problem. Each product had a set of vehicles which could carry the product and pickup and delivery could simultaneously occur. To solve the problem, two meta-heuristic methods...
متن کاملPalindromic Richness
In this paper, we study combinatorial and structural properties of a new class of finite and infinite words that are ‘rich’ in palindromes in the utmost sense. A characteristic property of so-called rich words is that all complete returns to any palindromic factor are themselves palindromes. These words encompass the well-known episturmian words, originally introduced by the second author toget...
متن کاملModified Padovan words and the maximum number of runs in a word
A run (or maximal periodicity) in a word is a periodic factor whose length is at least twice the period and which cannot be extended to the left or right without changing the period. Recently Kusano et al. [6] used a clever search technique to find run-rich words and were able to show that the number of runs in a word of length n can be greater than 0.94457564n. In this paper we use a two-stage...
متن کاملPeriodic Subwords in 2-piece Words
We find families of words W where W is a product of k pieces for k=2. For k=3,4,6, W arises in a small cancellation group with single defining relation W=1. We assume W involves generators but not their inverses and does not have a periodic cyclic permutation (like XY...XYX for nonempty base word XY). We prove W or W written backwards equals ABCD where ABC, CDA are periodic words with base word...
متن کاملRich Superstable Phenomena in a Piecewise Constant Nonautonomous Circuit with Impulsive Switching
This paper studies rich superstable phenomena in a nonautonomous piecewise constant circuit including one impulsive switch. Since the vector field of circuit equation is piecewise constant, embedded return map is piecewise linear and can be described explicitly in principle. As parameters vary the map can have infinite extrema with one flat segment. Such maps can cause complicated periodic orbi...
متن کامل