[{"page":"1-22","article_type":"original","arxiv":1,"has_accepted_license":"1","type":"journal_article","mathsc":["11J81","37B10","11J87"],"article_processing_charge":"Yes (in subscription journal)","fulldoi":"https://doi.org/10.1017/etds.2026.10324","language":[{"iso":"eng"}],"oa_version":"Published Version","keyword":["balanced-pair algorithm","Cobham’s conjecture","k-Bonacci words","Pisot conjecture","subspace theorem"],"_id":"22406","day":"10","doi":"10.1017/etds.2026.10324","main_file_link":[{"url":"https://doi.org/10.1017/etds.2026.10324","open_access":"1"}],"citation":{"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>","short":"P. Kebis, F. LUCA, J. OUAKNINE, A. SCOONES, J. WORRELL, Ergodic Theory and Dynamical Systems (2026) 1–22.","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>","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.","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>.","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>.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Transcendence for Pisot morphic words over an algebraic base","publication_identifier":{"issn":["0143-3857"],"eissn":["1469-4417"]},"publication_status":"epub_ahead","external_id":{"arxiv":["2405.05279"]},"publisher":"Cambridge University Press","author":[{"last_name":"Kebis","full_name":"Kebis, Pavol","id":"2e0132b3-4e98-11ef-b275-cf7281c2802a","first_name":"Pavol"},{"first_name":"FLORIAN","full_name":"LUCA, FLORIAN","last_name":"LUCA"},{"last_name":"OUAKNINE","full_name":"OUAKNINE, JOEL","first_name":"JOEL"},{"last_name":"SCOONES","full_name":"SCOONES, ANDREW","first_name":"ANDREW"},{"full_name":"WORRELL, JAMES","first_name":"JAMES","last_name":"WORRELL"}],"oa":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."}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"quality_controlled":"1","status":"public","OA_type":"hybrid","ddc":["000"],"PlanS_conform":"1","scopus_import":"1","publication":"Ergodic Theory and Dynamical Systems","year":"2026","researchdata_availability":"no","date_updated":"2026-08-03T06:17:50Z","das_tickbox":"0","department":[{"_id":"ToHe"},{"_id":"GradSch"}],"date_created":"2026-07-27T05:53:25Z","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.","date_published":"2026-07-10T00:00:00Z","month":"07","supplementarymaterial":"no","OA_place":"publisher"},{"das_tickbox":"0","date_updated":"2026-08-26T06:53:54Z","department":[{"_id":"GradSch"},{"_id":"TaHa"}],"date_created":"2026-08-12T13:29:17Z","acknowledgement":"I would like to thank the following people for fruitful discussions,\r\nhelpful sanity checks or comments on previous drafts: Roman Bezrukavnikov, Jens Niklas Eberhardt, Mischa Elkner, Tamás Hausel, Andres Fernandez Herrero, Adeel Khan,\r\nBernhard Köck, Andrei Konovalov, Quoc Ho, Mirko Mauri, Matthew Morrow, Charanya\r\nRavi, Kamil Rychlewicz, Shyiu Shen, Vladimir Sosnilo, Georg Tamme, Xinwen Zhu. I\r\nwould further like to thank Marc Hoyois and the anonymous referee for spotting an error\r\nin a previous version.\r\nThis work was done during author’s PhD at the Institute of Science and Technology Austria (ISTA). It was funded by a DOC Fellowship of the Austrian Academy\r\nof Sciences and by the Austrian Science Fund (FWF) 10.55776/P35847. For open access\r\npurposes, the author has applied a CC BY public copyright license to any author-accepted\r\nmanuscript version arising from this submission.","date_published":"2026-03-26T00:00:00Z","month":"03","OA_place":"publisher","supplementarymaterial":"no","publisher":"EMS Press","oa":1,"author":[{"id":"e3b80ae2-eb8e-11eb-b029-9aef4a9108a0","first_name":"Jakub","full_name":"Löwit, Jakub","last_name":"Löwit"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"We study torus-equivariant algebraic K-theory of affine Schubert varieties in the perfect affine Grassmannians over Fp. We further compare it to the torus-equivariant Hochschild homology of perfect complexes, which has a geometric description in terms of global functions on certain fixed-point schemes. We prove that Fp-linearly, this comparison is an isomorphism. Our approach is quite constructive, resulting in new computations of these K-theory rings. We establish various structural results for equivariant perfect algebraic K-theory on the way; we believe these are of independent interest."}],"corr_author":"1","PlanS_conform":"1","scopus_import":"1","ddc":["500"],"quality_controlled":"1","status":"public","OA_type":"hybrid","year":"2026","publication":"Documenta Mathematica","researchdata_availability":"no","main_file_link":[{"url":"https://doi.org/10.4171/DM/1064","open_access":"1"}],"citation":{"apa":"Löwit, J. (2026). Equivariant K-theory, affine Grassmannian and perfection. <i>Documenta Mathematica</i>. EMS Press. <a href=\"https://doi.org/10.4171/dm/1064\">https://doi.org/10.4171/dm/1064</a>","short":"J. Löwit, Documenta Mathematica (2026).","ama":"Löwit J. Equivariant K-theory, affine Grassmannian and perfection. <i>Documenta Mathematica</i>. 2026. doi:<a href=\"https://doi.org/10.4171/dm/1064\">10.4171/dm/1064</a>","ieee":"J. Löwit, “Equivariant K-theory, affine Grassmannian and perfection,” <i>Documenta Mathematica</i>. EMS Press, 2026.","mla":"Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” <i>Documenta Mathematica</i>, EMS Press, 2026, doi:<a href=\"https://doi.org/10.4171/dm/1064\">10.4171/dm/1064</a>.","chicago":"Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” <i>Documenta Mathematica</i>. EMS Press, 2026. <a href=\"https://doi.org/10.4171/dm/1064\">https://doi.org/10.4171/dm/1064</a>.","ista":"Löwit J. 2026. Equivariant K-theory, affine Grassmannian and perfection. Documenta Mathematica."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Equivariant K-theory, affine Grassmannian and perfection","external_id":{"arxiv":["2409.18925"]},"publication_status":"epub_ahead","publication_identifier":{"issn":["1431-0635"],"eissn":["1431-0643"]},"article_type":"original","arxiv":1,"related_material":{"record":[{"id":"22694","status":"public","relation":"dissertation_contains"}]},"type":"journal_article","project":[{"grant_number":"P35847","name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3"}],"has_accepted_license":"1","mathsc":["19E08","19L47","20G44","14G17","19D55","14F43","14L30","14D24","14M25"],"article_processing_charge":"Yes (in subscription journal)","keyword":["equivariant algebraic K-theory","perfection in positive characteristic","affine Grassmannian","affine Schubert varieties","Dennis trace map","equivariant Hochschild homology","fixed-point schemes","toric varieties"],"_id":"22693","day":"26","fulldoi":"https://doi.org/10.4171/dm/1064","oa_version":"Published Version","language":[{"iso":"eng"}],"doi":"10.4171/dm/1064"},{"citation":{"chicago":"El-Hayek, Antoine, Monika Henzinger, and Stefan Schmid. “Asymptotically Tight Bounds on the Time Complexity of Broadcast and Its Variants in Dynamic Networks.” In <i>14th Innovations in Theoretical Computer Science Conference</i>, edited by Yael Tauman Kalai, Vol. 251. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. <a href=\"https://doi.org/10.4230/LIPICS.ITCS.2023.47\">https://doi.org/10.4230/LIPICS.ITCS.2023.47</a>.","ista":"El-Hayek A, Henzinger M, Schmid S. 2023. Asymptotically tight bounds on the time complexity of broadcast and its variants in dynamic networks. 14th Innovations in Theoretical Computer Science Conference. ITCS: Innovations in Theoretical Computer Science, LIPIcs, vol. 251, 47.","short":"A. El-Hayek, M. Henzinger, S. Schmid, in:, Y. Tauman Kalai (Ed.), 14th Innovations in Theoretical Computer Science Conference, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.","ama":"El-Hayek A, Henzinger M, Schmid S. Asymptotically tight bounds on the time complexity of broadcast and its variants in dynamic networks. In: Tauman Kalai Y, ed. <i>14th Innovations in Theoretical Computer Science Conference</i>. Vol 251. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:<a href=\"https://doi.org/10.4230/LIPICS.ITCS.2023.47\">10.4230/LIPICS.ITCS.2023.47</a>","ieee":"A. El-Hayek, M. Henzinger, and S. Schmid, “Asymptotically tight bounds on the time complexity of broadcast and its variants in dynamic networks,” in <i>14th Innovations in Theoretical Computer Science Conference</i>, Cambridge, Massachusetts, USA, 2023, vol. 251.","mla":"El-Hayek, Antoine, et al. “Asymptotically Tight Bounds on the Time Complexity of Broadcast and Its Variants in Dynamic Networks.” <i>14th Innovations in Theoretical Computer Science Conference</i>, edited by Yael Tauman Kalai, vol. 251, 47, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:<a href=\"https://doi.org/10.4230/LIPICS.ITCS.2023.47\">10.4230/LIPICS.ITCS.2023.47</a>.","apa":"El-Hayek, A., Henzinger, M., &#38; Schmid, S. (2023). Asymptotically tight bounds on the time complexity of broadcast and its variants in dynamic networks. In Y. Tauman Kalai (Ed.), <i>14th Innovations in Theoretical Computer Science Conference</i> (Vol. 251). Cambridge, Massachusetts, USA: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.ITCS.2023.47\">https://doi.org/10.4230/LIPICS.ITCS.2023.47</a>"},"extern":"1","conference":{"end_date":"2023-01-13","location":"Cambridge, Massachusetts, USA","name":"ITCS: Innovations in Theoretical Computer Science","start_date":"2023-01-10"},"external_id":{"arxiv":["2211.10151"]},"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959772631"]},"publication_status":"published","title":"Asymptotically tight bounds on the time complexity of broadcast and its variants in dynamic networks","article_number":"47","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","type":"conference","has_accepted_license":"1","arxiv":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"22281"}]},"doi":"10.4230/LIPICS.ITCS.2023.47","keyword":["broadcast","cover","k-broadcast","dynamic radius","dynamic graphs","oblivious message adversary","time complexity","Theory of computation → Distributed algorithms","Networks → Network algorithms"],"_id":"22373","day":"01","oa_version":"Published Version","fulldoi":"https://doi.org/10.4230/LIPICS.ITCS.2023.47","language":[{"iso":"eng"}],"article_processing_charge":"No","date_created":"2026-07-20T11:45:04Z","acknowledgement":" This project has received funding from the European Research Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation programme (grant agreement No.\r\n101019564). This work was further supported by the Austrian Science Fund (FWF) and netIDEE\r\nSCIENCE project P 33775-N, as well as the FWF project I 4800-N (ADVISE)","editor":[{"first_name":"Yael","full_name":"Tauman Kalai, Yael","last_name":"Tauman Kalai"}],"date_updated":"2026-07-24T12:48:29Z","file":[{"file_size":1077427,"file_id":"22383","relation":"main_file","content_type":"application/pdf","checksum":"d7f45fdcbc5fccd61db69f56d775c636","success":1,"date_created":"2026-07-22T08:04:03Z","file_name":"2023_LIPIcs_El-Hayek.pdf","access_level":"open_access","date_updated":"2026-07-22T08:04:03Z","creator":"cchlebak"}],"month":"02","date_published":"2023-02-01T00:00:00Z","abstract":[{"text":"Data dissemination is a fundamental task in distributed computing. This paper studies broadcast problems in various innovative models where the communication network connecting n processes is dynamic (e.g., due to mobility or failures) and controlled by an adversary. \r\nIn the first model, the processes transitively communicate their ids in synchronous rounds along a rooted tree given in each round by the adversary whose goal is to maximize the number of rounds until at least one id is known by all processes. Previous research has shown a ⌈(3n-1)/2⌉-2 lower bound and an O(nlog log n) upper bound. We show the first linear upper bound for this problem, namely ⌈(1+√2) n-1⌉ ≈ 2.4n.\r\nWe extend these results to the setting where the adversary gives in each round k-disjoint forests and their goal is to maximize the number of rounds until there is a set of k ids such that each process knows of at least one of them. We give a ⌈3(n-k)/2⌉-1 lower bound and a (π²+6)/6 n+1 ≈ 2.6n upper bound for this problem.\r\nFinally, we study the setting where the adversary gives in each round a directed graph with k roots and their goal is to maximize the number of rounds until there exist k ids that are known by all processes. We give a ⌈3(n-3k)/2⌉+2 lower bound and a ⌈(1+√2)n⌉+k-1 ≈ 2.4n+k upper bound for this problem.\r\nFor the two latter problems no upper or lower bounds were previously known.","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"oa":1,"file_date_updated":"2026-07-22T08:04:03Z","author":[{"full_name":"El-Hayek, Antoine","id":"888a098e-fcac-11ee-aff7-d347be57b725","first_name":"Antoine","orcid":"0000-0003-4268-7368","last_name":"El-Hayek"},{"full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger"},{"full_name":"Schmid, Stefan","orcid":"0000-0002-7798-1711","first_name":"Stefan","last_name":"Schmid"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","alternative_title":["LIPIcs"],"volume":251,"year":"2023","publication":"14th Innovations in Theoretical Computer Science Conference","intvolume":"       251","scopus_import":"1","ddc":["000"],"quality_controlled":"1","status":"public"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"On a question of Vera T. Sós about size forcing of graphons","publication_identifier":{"eissn":["1588-2632"],"issn":["0236-5294"]},"publication_status":"published","external_id":{"isi":["000886839900006"],"arxiv":["2103.09114"]},"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2103.09114","open_access":"1"}],"citation":{"mla":"Cooley, Oliver, et al. “On a Question of Vera T. Sós about Size Forcing of Graphons.” <i>Acta Mathematica Hungarica</i>, vol. 168, Springer Nature, 2022, pp. 1–26, doi:<a href=\"https://doi.org/10.1007/s10474-022-01265-8\">10.1007/s10474-022-01265-8</a>.","ieee":"O. Cooley, M. Kang, and O. Pikhurko, “On a question of Vera T. Sós about size forcing of graphons,” <i>Acta Mathematica Hungarica</i>, vol. 168. Springer Nature, pp. 1–26, 2022.","ama":"Cooley O, Kang M, Pikhurko O. On a question of Vera T. Sós about size forcing of graphons. <i>Acta Mathematica Hungarica</i>. 2022;168:1-26. doi:<a href=\"https://doi.org/10.1007/s10474-022-01265-8\">10.1007/s10474-022-01265-8</a>","short":"O. Cooley, M. Kang, O. Pikhurko, Acta Mathematica Hungarica 168 (2022) 1–26.","apa":"Cooley, O., Kang, M., &#38; Pikhurko, O. (2022). On a question of Vera T. Sós about size forcing of graphons. <i>Acta Mathematica Hungarica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10474-022-01265-8\">https://doi.org/10.1007/s10474-022-01265-8</a>","ista":"Cooley O, Kang M, Pikhurko O. 2022. On a question of Vera T. Sós about size forcing of graphons. Acta Mathematica Hungarica. 168, 1–26.","chicago":"Cooley, Oliver, M. Kang, and O. Pikhurko. “On a Question of Vera T. Sós about Size Forcing of Graphons.” <i>Acta Mathematica Hungarica</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10474-022-01265-8\">https://doi.org/10.1007/s10474-022-01265-8</a>."},"article_processing_charge":"No","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1007/s10474-022-01265-8","oa_version":"Preprint","_id":"12151","keyword":["graphon","k-sample","graphon forcing","graph container"],"day":"23","doi":"10.1007/s10474-022-01265-8","page":"1-26","article_type":"original","isi":1,"arxiv":1,"type":"journal_article","date_published":"2022-11-23T00:00:00Z","month":"11","date_updated":"2024-10-09T21:03:37Z","department":[{"_id":"MaKw"}],"date_created":"2023-01-12T12:07:59Z","acknowledgement":"Supported by Austrian Science Fund (FWF) Grant I3747. Supported by ERC Advanced Grant 101020255 and Leverhulme Research Project Grant RPG-2018-424.\r\nAn extended abstract of this paper appeared in the Proceedings of the European Conference\r\non Combinatorics, Graph Theory and Applications (EuroComb 2021), CRM Research Perspectives, Springer.","status":"public","quality_controlled":"1","scopus_import":"1","intvolume":"       168","publication":"Acta Mathematica Hungarica","volume":168,"year":"2022","publisher":"Springer Nature","author":[{"first_name":"Oliver","id":"43f4ddd0-a46b-11ec-8df6-ef3703bd721d","full_name":"Cooley, Oliver","last_name":"Cooley"},{"last_name":"Kang","first_name":"M.","full_name":"Kang, M."},{"last_name":"Pikhurko","first_name":"O.","full_name":"Pikhurko, O."}],"oa":1,"corr_author":"1","abstract":[{"text":"The k-sample G(k,W) from a graphon W:[0,1]2→[0,1] is the random graph on {1,…,k}, where we sample x1,…,xk∈[0,1] uniformly at random and make each pair {i,j}⊆{1,…,k} an edge with probability W(xi,xj), with all these choices being mutually independent. Let the random variable Xk(W) be the number of edges in  G(k,W). Vera T. Sós asked in 2012 whether two graphons U, W are necessarily weakly isomorphic if the random variables Xk(U) and Xk(W) have the same distribution for every integer k≥2. This question when one of the graphons W is a constant function was answered positively by Endre Csóka and independently by Jacob Fox, Tomasz Łuczak and Vera T. Sós. Here we investigate the question when W is a 2-step graphon and prove that the answer is positive for a 3-dimensional family of such graphons. We also present some related results.","lang":"eng"}]}]