[{"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2405.05279"]},"publisher":"Cambridge University Press","status":"public","has_accepted_license":"1","day":"10","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"We thank the anonymous referee for identifying an error in an earlier\r\nversion of the paper. We gratefully acknowledge support from UKRI Frontier Research\r\nGrant EP/X033813/1, ERC grant DynAMiCS (101167561) and DFG grant 389792660 as\r\npart of TRR 248. J.O. is also affiliated with Keble College, Oxford as an Emmy Network\r\nfellow.","publication_status":"epub_ahead","mathsc":["11J81","37B10","11J87"],"OA_place":"publisher","PlanS_conform":"1","title":"Transcendence for Pisot morphic words over an algebraic base","_id":"22406","oa_version":"Published Version","citation":{"ista":"Kebis P, LUCA F, OUAKNINE J, SCOONES A, WORRELL J. 2026. Transcendence for Pisot morphic words over an algebraic base. Ergodic Theory and Dynamical Systems., 1–22.","ieee":"P. Kebis, F. LUCA, J. OUAKNINE, A. SCOONES, and J. WORRELL, “Transcendence for Pisot morphic words over an algebraic base,” <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press, pp. 1–22, 2026.","chicago":"Kebis, Pavol, FLORIAN LUCA, JOEL OUAKNINE, ANDREW SCOONES, and JAMES WORRELL. “Transcendence for Pisot Morphic Words over an Algebraic Base.” <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press, 2026. <a href=\"https://doi.org/10.1017/etds.2026.10324\">https://doi.org/10.1017/etds.2026.10324</a>.","short":"P. Kebis, F. LUCA, J. OUAKNINE, A. SCOONES, J. WORRELL, Ergodic Theory and Dynamical Systems (2026) 1–22.","mla":"Kebis, Pavol, et al. “Transcendence for Pisot Morphic Words over an Algebraic Base.” <i>Ergodic Theory and Dynamical Systems</i>, Cambridge University Press, 2026, pp. 1–22, doi:<a href=\"https://doi.org/10.1017/etds.2026.10324\">10.1017/etds.2026.10324</a>.","apa":"Kebis, P., LUCA, F., OUAKNINE, J., SCOONES, A., &#38; WORRELL, J. (2026). Transcendence for Pisot morphic words over an algebraic base. <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/etds.2026.10324\">https://doi.org/10.1017/etds.2026.10324</a>","ama":"Kebis P, LUCA F, OUAKNINE J, SCOONES A, WORRELL J. Transcendence for Pisot morphic words over an algebraic base. <i>Ergodic Theory and Dynamical Systems</i>. 2026:1-22. doi:<a href=\"https://doi.org/10.1017/etds.2026.10324\">10.1017/etds.2026.10324</a>"},"date_published":"2026-07-10T00:00:00Z","article_processing_charge":"Yes (in subscription journal)","date_updated":"2026-07-27T06:47:17Z","oa":1,"doi":"10.1017/etds.2026.10324","article_type":"original","quality_controlled":"1","abstract":[{"lang":"eng","text":"It is known that for a uniform morphic sequence 𝒖 =⟨𝑢𝑛⟩∞\r\n𝑛=0 and an algebraic number 𝛽 such that |𝛽| >1, the number [[𝒖]]𝛽 :=∑∞\r\n𝑛=0(𝑢𝑛/𝛽𝑛) either lies in ℚ⁡(𝛽) or is transcendental. In this paper, we show a similar rational–transcendental dichotomy for sequences defined by irreducible Pisot morphisms on binary alphabets. Subject to the Pisot conjecture (an irreducible Pisot morphism has pure discrete spectrum), we generalise the latter result to arbitrary finite alphabets. In certain cases, we are able to show transcendence of [[𝒖]]𝛽 outright. In particular, for 𝑘 ≥2, if 𝒖 is the k-Bonacci word, then [[𝒖]]𝛽 is transcendental."}],"publication":"Ergodic Theory and Dynamical Systems","ddc":["000"],"OA_type":"hybrid","arxiv":1,"type":"journal_article","scopus_import":"1","year":"2026","publication_identifier":{"eissn":["1469-4417"],"issn":["0143-3857"]},"das_tickbox":"0","month":"07","keyword":["balanced-pair algorithm","Cobham’s conjecture","k-Bonacci words","Pisot conjecture","subspace theorem"],"main_file_link":[{"url":"https://doi.org/10.1017/etds.2026.10324","open_access":"1"}],"supplementarymaterial":"no","page":"1-22","researchdata_availability":"no","department":[{"_id":"ToHe"},{"_id":"GradSch"}],"date_created":"2026-07-27T05:53:25Z","language":[{"iso":"eng"}],"author":[{"last_name":"Kebis","full_name":"Kebis, Pavol","id":"2e0132b3-4e98-11ef-b275-cf7281c2802a","first_name":"Pavol"},{"last_name":"LUCA","full_name":"LUCA, FLORIAN","first_name":"FLORIAN"},{"full_name":"OUAKNINE, JOEL","last_name":"OUAKNINE","first_name":"JOEL"},{"full_name":"SCOONES, ANDREW","last_name":"SCOONES","first_name":"ANDREW"},{"full_name":"WORRELL, JAMES","last_name":"WORRELL","first_name":"JAMES"}]}]