| Autor: |
Maithilee Patawar, Kalpesh Kapoor |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Trends in Mathematics ISBN: 9783030838225 |
| DOI: |
10.1007/978-3-030-83823-2_79 |
| Popis: |
A square is a concatenation of two identical words. A long-standing open conjecture is that the number of distinct squares in a word is bounded by its length. When two squares start at a location for the last time in a word, the longer square is called FS-double square. One way to increase the number of distinct squares in a word is to add as many FS-double squares as possible. For any FS-double square, the first letter always adds two distinct squares. However, the last letter can be in at most two distinct squares. We give a structure of an FS-double square where removing any of the terminal letters removes two distinct squares. We show that the maximum number of such FS-double squares that are adjacent to each other in a word w is less than \(\frac{|w|}{11}\). We also show that the distinct squares introduced by the terminal letters of an FS-double square are conjugates. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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