تقرير
The Length of the Longest Sequence of Consecutive FS-double Squares in a word
| العنوان: | The Length of the Longest Sequence of Consecutive FS-double Squares in a word |
|---|---|
| المؤلفون: | Patawar, M., Kapoor, K. |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 68R15, G.2.1, F.2.2 |
| الوصف: | A square is a concatenation of two identical words, and a word $w$ is said to have a square $yy$ if $w$ can be written as $xyyz$ for some words $x$ and $z$. It is known that the ratio of the number of distinct squares in a word to its length is less than two and any location of a word could begin with at most two rightmost distinct squares. A square whose first location starts with the last occurrence of two distinct squares is an FS-double square. We explore and identify the conditions to generate a sequence of locations in a word that starts with FS-double squares. We first find the structure of the smallest word that begins with two consecutive FS-double squares and obtain its properties that enable to extend the sequence of FS-double squares. It is proved that the length of the longest sequence of consecutive FS-double squares in a word of length $n$ is at most $\frac{n}{7}$. We show that the squares in the longest sequence of consecutive FS-double squares are conjugates. Comment: 19 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2107.07473 |
| رقم الأكسشن: | edsarx.2107.07473 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |