{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:04:58Z","timestamp":1776841498276,"version":"3.51.2"},"reference-count":38,"publisher":"American Mathematical Society (AMS)","issue":"360","license":[{"start":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T00:00:00Z","timestamp":1780963200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V032003\/1"],"award-info":[{"award-number":["EP\/V032003\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We show that the Diophantine problem in Thompson\u2019s group\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper F\">\n                        <mml:semantics>\n                          <mml:mi>F<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">F<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is undecidable. Our proof uses the facts that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper F\">\n                        <mml:semantics>\n                          <mml:mi>F<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">F<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    has finite commutator width and rank\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2\">\n                        <mml:semantics>\n                          <mml:mn>2<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    abelianisation, then uses similar arguments used by B\u00fcchi and Senger [Z. Math. Logik Grundlag. Math. 34 (1988), pp. 337\u2013342] and Ciobanu and Garreta [Int. Math. Res. Not. IMRN 5 (2024), pp. 4119\u20134159] to show the Diophantine problem in free groups and monoids with abelianisation constraints is undecidable.\n                  <\/p>","DOI":"10.1090\/mcom\/4113","type":"journal-article","created":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T15:57:17Z","timestamp":1749484637000},"page":"2013-2023","source":"Crossref","is-referenced-by-count":0,"title":["The Diophantine problem in Thompson\u2019s group \ud835\udc39"],"prefix":"10.1090","volume":"95","author":[{"given":"Luna","family":"Elliott","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alex","family":"Levine","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2025,6,9]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1016\/j.jpaa.2007.02.011","article-title":"Interpreting the arithmetic in Thompson\u2019s group \ud835\udc39","volume":"211","author":"Bardakov, Valery","year":"2007","journal-title":"J. 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