منابع مشابه
Generalized trapezoidal words
The factor complexity function C w (n) of a finite or infinite word w counts the number of distinct factors of w of length n for each n ≥ 0. A finite word w of length |w| is said to be trapezoidal if the graph of its factor complexity C w (n) as a function of n (for 0 ≤ n ≤ |w|) is that of a regular trapezoid (or possibly an isosceles triangle); that is, C w (n) increases by 1 with each n on so...
متن کاملA Classification of Trapezoidal Words
Trapezoidal words are finite words having at most n+1 distinct factors of length n, for every n≥ 0. They encompass finite Sturmian words. We distinguish trapezoidal words into two disjoint subsets: open and closed trapezoidal words. A trapezoidal word is closed if its longest repeated prefix has exactly two occurrences in the word, the second one being a suffix of the word. Otherwise it is open...
متن کاملRich, Sturmian, and trapezoidal words
In this paper we explore various interconnections between rich words, Sturmian words, and trapezoidal words. Rich words, first introduced by the second and third authors together with J. Justin and S. Widmer, constitute a new class of finite and infinite words characterized by having the maximal number of palindromic factors. Every finite Sturmian word is rich, but not conversely. Trapezoidal w...
متن کاملGeneralized Trapezoidal Distributions
We present a construction and basic properties of a class of continuous distributions of an arbitrary form defined on a compact (bounded) set by concatenating in a continuous manner three probability density functions with bounded support using a modified mixture technique. These three distributions may represent growth, stability and decline stages of a physical or mental phenomenon.
متن کاملEnumeration and structure of trapezoidal words
Trapezoidal words are words having at most n+1 distinct factors of length n for every n ≥ 0. They therefore encompass finite Sturmian words. We give combinatorial characterizations of trapezoidal words and exhibit a formula for their enumeration. We then separate trapezoidal words into two disjoint classes: open and closed. A trapezoidal word is closed if it has a factor that occurs only as a p...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2015
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2015.06.008