A combinatorial problem on Trapezoidal words
نویسندگان
چکیده
منابع مشابه
A 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 کاملGeneralized 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 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...
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Let M be a set and F a family of its subsets. F is said by E. W. MILLER [5] to possess property B if there exists a subset K of M so that no set of the family F is contained either in K or in K (K is the complement of K in M) . HAJNAL and 1 [2] recently published a paper on the property B and its generalisations . One of the unsolved problems we state asks : What is the smallest integer in (n) ...
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: Theoretical Computer Science
سال: 2002
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(00)00431-x