{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:46:06Z","timestamp":1776836766766,"version":"3.51.2"},"reference-count":11,"publisher":"American Mathematical Society (AMS)","issue":"341","license":[{"start":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T00:00:00Z","timestamp":1706659200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100003074","name":"Agencia Nacional de Promoci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","doi-asserted-by":"publisher","award":["PICT 2018-2315"],"award-info":[{"award-number":["PICT 2018-2315"]}],"id":[{"id":"10.13039\/501100003074","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100017585","name":"Consejo Interuniversitario Nacional","doi-asserted-by":"publisher","award":["PICT 2018-2315"],"award-info":[{"award-number":["PICT 2018-2315"]}],"id":[{"id":"10.13039\/100017585","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Years ago Zeev Rudnick defined the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -Poisson generic sequences as the infinite sequences of symbols in a finite alphabet where the number of occurrences of long words in the initial segments follow the Poisson distribution with parameter\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Although almost all sequences, with respect to the uniform measure, are Poisson generic, no explicit instance has yet been given. In this note we give a construction of an explicit\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -Poisson generic sequence over any alphabet and any positive\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , except for the case of the two-symbol alphabet, in which it is required that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    be less than or equal to the natural logarithm of\u00a0\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                    . Since\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -Poisson genericity implies Borel normality, the constructed sequences are Borel normal. The same construction provides explicit instances of Borel normal sequences that are not\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -Poisson generic.\n                  <\/p>","DOI":"10.1090\/mcom\/3806","type":"journal-article","created":{"date-parts":[[2022,11,9]],"date-time":"2022-11-09T11:46:50Z","timestamp":1667994410000},"page":"1453-1466","source":"Crossref","is-referenced-by-count":3,"title":["A construction of a \ud835\udf06-Poisson generic sequence"],"prefix":"10.1090","volume":"92","author":[{"given":"Ver\u00f3nica","family":"Becher","sequence":"first","affiliation":[]},{"given":"Gabriel","family":"Sac Himelfarb","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,1,31]]},"reference":[{"key":"1","unstructured":"N. Alvarez, V. Becher, and M. Mereb, Poisson generic sequences, Int. Math. Res. Not. rnac234 (2022), DOI 10.1093\/imrn\/rnac234."},{"issue":"18","key":"2","doi-asserted-by":"publisher","first-page":"930","DOI":"10.1016\/j.ipl.2011.06.013","article-title":"On extending de Bruijn sequences","volume":"111","author":"Becher, Ver\u00f3nica","year":"2011","journal-title":"Inform. Process. Lett.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-0190","issn-type":"print"},{"key":"3","series-title":"Cambridge Tracts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139017732","volume-title":"Distribution modulo one and Diophantine approximation","volume":"193","author":"Bugeaud, Yann","year":"2012","ISBN":"https:\/\/id.crossref.org\/isbn\/9780521111690"},{"key":"4","unstructured":"L. P. Colomer, Very normal numbers, 2019, Tesis de Licenciatura en Ciencias de la Computaci\u00f3n, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires."},{"key":"5","doi-asserted-by":"publisher","first-page":"857","DOI":"10.1090\/S0002-9904-1946-08657-7","article-title":"Note on normal numbers","volume":"52","author":"Copeland, Arthur H.","year":"1946","journal-title":"Bull. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9904","issn-type":"print"},{"key":"6","first-page":"758","article-title":"A combinatorial problem","volume":"49","author":"de Bruijn, N. G.","year":"1946","journal-title":"Nederl. Akad. Wetensch., Proc.","ISSN":"https:\/\/id.crossref.org\/issn\/0370-0348","issn-type":"print"},{"issue":"4","key":"7","doi-asserted-by":"publisher","first-page":"373","DOI":"10.2307\/2324917","article-title":"Unsolved Problems: A Pseudorandom Sequence\u2013How Random Is It?","volume":"99","author":"Ehrenfeucht, Andrzej","year":"1992","journal-title":"Amer. Math. Monthly","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9890","issn-type":"print"},{"key":"8","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801655","volume-title":"Analytic combinatorics","author":"Flajolet, Philippe","year":"2009","ISBN":"https:\/\/id.crossref.org\/isbn\/9780521898065"},{"key":"9","series-title":"Pure and Applied Mathematics","volume-title":"Uniform distribution of sequences","author":"Kuipers, L.","year":"1974"},{"issue":"5","key":"10","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1515\/form.2002.030","article-title":"The distribution of spacings between fractional parts of lacunary sequences","volume":"14","author":"Rudnick, Ze\u00e9v","year":"2002","journal-title":"Forum Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0933-7741","issn-type":"print"},{"key":"11","unstructured":"Benjamin Weiss, Poisson generic points, Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness, Centre International de Rencontres Math\u00e9matiques, November 23 to 29, 2020. Audio-visual resource: doi:10.24350\/CIRM.V.19690103."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-341\/S0025-5718-2023-03806-6\/mcom3806_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-341\/S0025-5718-2023-03806-6\/S0025-5718-2023-03806-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:55:40Z","timestamp":1776833740000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-341\/S0025-5718-2023-03806-6\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,31]]},"references-count":11,"journal-issue":{"issue":"341","published-print":{"date-parts":[[2023,5]]}},"alternative-id":["S0025-5718-2023-03806-6"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3806","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2023,1,31]]}}}