Novel Constructions of Words with Strong Avoidance Properties and their Combinatorial Analysis
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910947996598272 |
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| author | Abdullah, Duaa Hamoud, Jasem |
| author_facet | Abdullah, Duaa Hamoud, Jasem |
| contents | This paper begins with a comprehensive overview of combinatorics on words and symbolic dynamics, covering their historical origins, fundamental concepts, and interconnections. Building upon this foundation, we introduce novel mathematical constructions related to pattern avoidance in infinite words. Specifically, we define Strongly $(k, δ)$-Free Words generated via cyclic shift morphisms and present a theorem establishing specific avoidance properties for these words, along with a detailed proof. Furthermore, we propose a conjecture regarding their factor complexity. These original results contribute to the theoretical understanding of word structures and their combinatorial properties, opening avenues for further research in discrete mathematics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Novel Constructions of Words with Strong Avoidance Properties and their Combinatorial Analysis Abdullah, Duaa Hamoud, Jasem Combinatorics 68R15, 11B39, 05A05, 68R15, 37B10 F.2.2 This paper begins with a comprehensive overview of combinatorics on words and symbolic dynamics, covering their historical origins, fundamental concepts, and interconnections. Building upon this foundation, we introduce novel mathematical constructions related to pattern avoidance in infinite words. Specifically, we define Strongly $(k, δ)$-Free Words generated via cyclic shift morphisms and present a theorem establishing specific avoidance properties for these words, along with a detailed proof. Furthermore, we propose a conjecture regarding their factor complexity. These original results contribute to the theoretical understanding of word structures and their combinatorial properties, opening avenues for further research in discrete mathematics. |
| title | Novel Constructions of Words with Strong Avoidance Properties and their Combinatorial Analysis |
| topic | Combinatorics 68R15, 11B39, 05A05, 68R15, 37B10 F.2.2 |
| url | https://arxiv.org/abs/2505.11403 |