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The Billaud Conjecture for |Σ| = 4, and beyond
The Billaud Conjecture, first stated in 1993, is a fundamental problem on finite words and their heirs, i.e., the words obtained by a projection deleting a single letter. The conjecture states that every morphically primitive word, i.e., a word which is not a fixed point of any non-identity morphism...
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| Main Authors: | , |
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| Format: | Default Conference proceeding |
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2022
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| Online Access: | https://hdl.handle.net/2134/19907065.v1 |
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| _version_ | 1818165949802479616 |
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| author | Szymon Lopaciuk Daniel Reidenbach |
| author_facet | Szymon Lopaciuk Daniel Reidenbach |
| author_sort | Szymon Lopaciuk (7050638) |
| collection | Figshare |
| description | The Billaud Conjecture, first stated in 1993, is a fundamental problem on finite words and their heirs, i.e., the words obtained by a projection deleting a single letter. The conjecture states that every morphically primitive word, i.e., a word which is not a fixed point of any non-identity morphism, has at least one morphically primitive heir. In this paper we give the proof of the Conjecture for alphabet size 4, and discuss the potential for generalising our reasoning to larger alphabets. We briefly discuss how other language-theoretic tools relate to the Conjecture, and their suitability for potential generalisations. |
| format | Default Conference proceeding |
| id | rr-article-19907065 |
| institution | Loughborough University |
| publishDate | 2022 |
| record_format | Figshare |
| spelling | rr-article-199070652022-05-06T00:00:00Z The Billaud Conjecture for |Σ| = 4, and beyond Szymon Lopaciuk (7050638) Daniel Reidenbach (1256598) Billaud Conjecture Morphic primitivity Fixed point <p>The Billaud Conjecture, first stated in 1993, is a fundamental problem on finite words and their heirs, i.e., the words obtained by a projection deleting a single letter. The conjecture states that every morphically primitive word, i.e., a word which is not a fixed point of any non-identity morphism, has at least one morphically primitive heir. In this paper we give the proof of the Conjecture for alphabet size 4, and discuss the potential for generalising our reasoning to larger alphabets. We briefly discuss how other language-theoretic tools relate to the Conjecture, and their suitability for potential generalisations.</p> 2022-05-06T00:00:00Z Text Conference contribution 2134/19907065.v1 https://figshare.com/articles/conference_contribution/The_Billaud_Conjecture_for_4_and_beyond/19907065 All Rights Reserved |
| spellingShingle | Billaud Conjecture Morphic primitivity Fixed point Szymon Lopaciuk Daniel Reidenbach The Billaud Conjecture for |Σ| = 4, and beyond |
| title | The Billaud Conjecture for |Σ| = 4, and beyond |
| title_full | The Billaud Conjecture for |Σ| = 4, and beyond |
| title_fullStr | The Billaud Conjecture for |Σ| = 4, and beyond |
| title_full_unstemmed | The Billaud Conjecture for |Σ| = 4, and beyond |
| title_short | The Billaud Conjecture for |Σ| = 4, and beyond |
| title_sort | billaud conjecture for |σ| = 4, and beyond |
| topic | Billaud Conjecture Morphic primitivity Fixed point |
| url | https://hdl.handle.net/2134/19907065.v1 |