The Thue-Morse Transform
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918529357316096 |
|---|---|
| author | Cloitre, Benoit |
| author_facet | Cloitre, Benoit |
| contents | We define the Thue-Morse transform T on a class of infinite binary words. It sends the alternating word a_0 = 010101... to the Thue-Morse sequence. We then study its orbit a_m = T^m(a_0) as well as the sequences u_m and v_m giving respectively the positions of the ones and the zeros in a_m. We obtain an explicit formula for a_m and deduce Prouhet-Tarry-Escott identities for the partitions induced by u_m and v_m. We also give composition formulas for u_m and v_m, and a full description of the factor complexity of a_m. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06243 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Thue-Morse Transform Cloitre, Benoit Number Theory 11B85 (Primary), 68R15, 11A63, 11D72, 11B83 (Secondary) We define the Thue-Morse transform T on a class of infinite binary words. It sends the alternating word a_0 = 010101... to the Thue-Morse sequence. We then study its orbit a_m = T^m(a_0) as well as the sequences u_m and v_m giving respectively the positions of the ones and the zeros in a_m. We obtain an explicit formula for a_m and deduce Prouhet-Tarry-Escott identities for the partitions induced by u_m and v_m. We also give composition formulas for u_m and v_m, and a full description of the factor complexity of a_m. |
| title | The Thue-Morse Transform |
| topic | Number Theory 11B85 (Primary), 68R15, 11A63, 11D72, 11B83 (Secondary) |
| url | https://arxiv.org/abs/2604.06243 |