منابع مشابه
Words with many Palindrome Pair Factors
Motivated by a conjecture of Frid, Puzynina, and Zamboni, we investigate infinite words with the property that for infinitely many n, every length-n factor is a product of two palindromes. We show that every Sturmian word has this property, but this does not characterize the class of Sturmian words. We also show that the Thue–Morse word does not have this property. We investigate finite words w...
متن کاملInfinite words without palindrome
We show that there exists an uniformly recurrent infinite word whose set of factors is closed under reversal and which has only finitely many palindromic factors. 1 Notations For a finite word w = w1 · · ·wn, the reversal of w is the word w̃ = wn · · ·w1. This notation is extended to sets by setting F = {w̃ | w ∈ F} for any set F of finite words. A word w is a palindrome if w̃ = w. A set F of fini...
متن کاملPalindrome Prefixes and Episturmian Words
Let w be an infinite word on an alphabet A. We denote by (ni)i≥1 the increasing sequence (assumed to be infinite) of all lengths of palindrome prefixes of w. In this text, we give an explicit construction of all words w such that ni+1 ≤ 2ni + 1 for all i, and study these words. Special examples include characteristic Sturmian words, and more generally standard episturmian words. As an applicati...
متن کاملCubefree words with many squares
We construct infinite cubefree binary words containing exponentially many distinct squares of length n. We also show that for every positive integer n, there is a cubefree binary square of length 2n.
متن کاملCharacterizations of Words with Many Periods
In 2001 Droubay, Justin and Pirillo studied the so-called standard episturmian words. In 2006 and 2007 Fischler defined another type of words in the framework of simultaneous diophantine approximation. Both classes of words were described in terms of palindromic prefixes of infinite words. In 2003 the authors introduced words which they called extremal FW words after they had met so-called FW w...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/5583