---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22406'
abstract:
- lang: eng
  text: "It is known that for a uniform morphic sequence \U0001D496 =⟨\U0001D462\U0001D45B⟩∞\r\n\U0001D45B=0
    and an algebraic number \U0001D6FD such that |\U0001D6FD| >1, the number [[\U0001D496]]\U0001D6FD
    :=∑∞\r\n\U0001D45B=0(\U0001D462\U0001D45B/\U0001D6FD\U0001D45B) either lies in
    ℚ⁡(\U0001D6FD) 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 [[\U0001D496]]\U0001D6FD outright.
    In particular, for \U0001D458 ≥2, if \U0001D496 is the k-Bonacci word, then [[\U0001D496]]\U0001D6FD
    is transcendental."
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."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Pavol
  full_name: Kebis, Pavol
  id: 2e0132b3-4e98-11ef-b275-cf7281c2802a
  last_name: Kebis
- first_name: FLORIAN
  full_name: LUCA, FLORIAN
  last_name: LUCA
- first_name: JOEL
  full_name: OUAKNINE, JOEL
  last_name: OUAKNINE
- first_name: ANDREW
  full_name: SCOONES, ANDREW
  last_name: SCOONES
- first_name: JAMES
  full_name: WORRELL, JAMES
  last_name: WORRELL
citation:
  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>
  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>
  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>.
  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.
  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.
  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>.
  short: P. Kebis, F. LUCA, J. OUAKNINE, A. SCOONES, J. WORRELL, Ergodic Theory and
    Dynamical Systems (2026) 1–22.
das_tickbox: '0'
date_created: 2026-07-27T05:53:25Z
date_published: 2026-07-10T00:00:00Z
date_updated: 2026-07-27T06:47:17Z
day: '10'
ddc:
- '000'
department:
- _id: ToHe
- _id: GradSch
doi: 10.1017/etds.2026.10324
external_id:
  arxiv:
  - '2405.05279'
has_accepted_license: '1'
keyword:
- balanced-pair algorithm
- Cobham’s conjecture
- k-Bonacci words
- Pisot conjecture
- subspace theorem
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1017/etds.2026.10324
mathsc:
- 11J81
- 37B10
- 11J87
month: '07'
oa: 1
oa_version: Published Version
page: 1-22
publication: Ergodic Theory and Dynamical Systems
publication_identifier:
  eissn:
  - 1469-4417
  issn:
  - 0143-3857
publication_status: epub_ahead
publisher: Cambridge University Press
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Transcendence for Pisot morphic words over an algebraic base
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...