{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:35:52Z","timestamp":1740137752160,"version":"3.37.3"},"reference-count":12,"publisher":"EDP Sciences","issue":"1","license":[{"start":{"date-parts":[[2016,6,2]],"date-time":"2016-06-02T00:00:00Z","timestamp":1464825600000},"content-version":"vor","delay-in-days":153,"URL":"https:\/\/www.edpsciences.org\/en\/authors\/copyright-and-licensing"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["MuDeRa (FWF-ANR)"],"award-info":[{"award-number":["MuDeRa (FWF-ANR)"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009475","name":"Conseil R\u00e9gional de Lorraine","doi-asserted-by":"crossref","award":["AAP-086-214"],"award-info":[{"award-number":["AAP-086-214"]}],"id":[{"id":"10.13039\/501100009475","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Theor. Inf. Appl."],"accepted":{"date-parts":[[2016,3,24]]},"published-print":{"date-parts":[[2016,1]]},"abstract":"<jats:p>Let <jats:italic>P<\/jats:italic>(<jats:italic>x<\/jats:italic>) \u2208 \u2124\n              [<jats:italic>x<\/jats:italic>] be an integer-valued polynomial taking only\n          positive values and let <jats:italic>d<\/jats:italic> be a fixed positive integer. The aim of this short\n          note is to show, by elementary means, that for any sufficiently large integer\n            <jats:italic>N<\/jats:italic> \u2265\n              <jats:italic>N<\/jats:italic><jats:sub>0<\/jats:sub>(<jats:italic>P,d<\/jats:italic>) there exists\n            <jats:italic>n<\/jats:italic> such that\n            <jats:italic>P<\/jats:italic>(<jats:italic>n<\/jats:italic>) contains <jats:italic>exactly\n            <\/jats:italic><jats:italic>N<\/jats:italic>\n          occurrences of the block (<jats:italic>q<\/jats:italic> \u2212\n              1<jats:italic>, q<\/jats:italic> \u2212 1,<jats:italic>...<\/jats:italic><jats:italic>, q<\/jats:italic> \u2212\n            1) of size <jats:italic>d<\/jats:italic> in its digital expansion in base <jats:italic>q<\/jats:italic>. The method of proof\n          allows to give a lower estimate on the number of \u201c0\u201d resp. \u201c1\u201d symbols in polynomial\n          extractions in the Rudin\u2013Shapiro sequence.<\/jats:p>","DOI":"10.1051\/ita\/2016009","type":"journal-article","created":{"date-parts":[[2016,6,2]],"date-time":"2016-06-02T02:32:10Z","timestamp":1464834730000},"page":"93-99","source":"Crossref","is-referenced-by-count":1,"title":["On digital blocks of polynomial values and extractions in the Rudin\u2013Shapiro sequence"],"prefix":"10.1051","volume":"50","author":[{"given":"Thomas","family":"Stoll","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2016,6,2]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"J.-P. Allouche and J. Shallit, Automatic Sequences:\n          Theory, Applications, Generalizations. Cambridge University Press, Cambridge (2003).","DOI":"10.1017\/CBO9780511546563"},{"key":"R2","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1080\/00029890.1996.12004830","volume":"103","author":"Brillhart","year":"1996","journal-title":"Amer. Math. Monthly"},{"key":"R3","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1112\/S0024609305017789","volume":"38","author":"Dartyge","year":"2006","journal-title":"Bull. London Math. Soc."},{"key":"R4","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1016\/j.disc.2007.03.069","volume":"308","author":"Drmota","year":"2008","journal-title":"Discrete Math."},{"key":"R5","doi-asserted-by":"crossref","first-page":"259","DOI":"10.4064\/aa-13-3-259-265","volume":"13","author":"Gelfond","year":"1967","journal-title":"Acta Arith."},{"key":"R6","doi-asserted-by":"crossref","unstructured":"M. Lothaire, Applied Combinatorics on Words. Vol.\n          105 of Encycl. Math. Appl. Cambridge University Press, Cambridge (2005).","DOI":"10.1017\/CBO9781107341005"},{"key":"R7","doi-asserted-by":"crossref","first-page":"2595","DOI":"10.4171\/JEMS\/566","volume":"27","author":"Mauduit","year":"2015","journal-title":"J. Eur. Math. Soc."},{"key":"R8","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1090\/S0002-9939-1969-0244149-8","volume":"21","author":"Newman","year":"1969","journal-title":"Proc. Amer. Math. Soc."},{"key":"R9","unstructured":"The Online Encyclopedia of Integer Sequences\n          (OEIS), edited by N.J.A. Sloane. Available at https:\/\/oeis.org\/."},{"key":"R10","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1090\/S0002-9939-1959-0116184-5","volume":"10","author":"Rudin","year":"1959","journal-title":"Proc. Amer. Math. Soc."},{"key":"R11","unstructured":"H.S. Shapiro, Extremal Problems for\n            Polynomials and Power Series. Master thesis, M.I.T. (1951)."},{"key":"R12","first-page":"233","volume":"47","author":"Stoll","year":"2012","journal-title":"Functiones et Approximatio"}],"container-title":["RAIRO - Theoretical Informatics and Applications"],"original-title":[],"link":[{"URL":"http:\/\/www.rairo-ita.org\/10.1051\/ita\/2016009\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,3]],"date-time":"2021-09-03T07:53:59Z","timestamp":1630655639000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.rairo-ita.org\/10.1051\/ita\/2016009"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1]]},"references-count":12,"journal-issue":{"issue":"1"},"alternative-id":["ita160027"],"URL":"https:\/\/doi.org\/10.1051\/ita\/2016009","relation":{},"ISSN":["0988-3754","1290-385X"],"issn-type":[{"type":"print","value":"0988-3754"},{"type":"electronic","value":"1290-385X"}],"subject":[],"published":{"date-parts":[[2016,1]]}}}