{"id":"https://openalex.org/W1507366302","doi":"https://doi.org/10.37236/1196","title":"How Many Squares Must a Binary Sequence Contain?","display_name":"How Many Squares Must a Binary Sequence Contain?","publication_year":1994,"publication_date":"1994-12-11","ids":{"openalex":"https://openalex.org/W1507366302","doi":"https://doi.org/10.37236/1196","mag":"1507366302"},"language":"en","primary_location":{"id":"doi:10.37236/1196","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1196","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r2/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r2/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061322084","display_name":"Aviezri S. Fraenkel","orcid":null},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Aviezri S. Fraenkel","raw_affiliation_strings":["Department of Applied Mathematics & Computer Science, The Weizmann Institute of Science, Rehovot 76100, Israel","Weizmann Institute of Science"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics & Computer Science, The Weizmann Institute of Science, Rehovot 76100, Israel","institution_ids":["https://openalex.org/I53964585"]},{"raw_affiliation_string":"Weizmann Institute of Science","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009872989","display_name":"R. J. Simpson","orcid":null},"institutions":[{"id":"https://openalex.org/I205640436","display_name":"Curtin University","ror":"https://ror.org/02n415q13","country_code":"AU","type":"education","lineage":["https://openalex.org/I205640436"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"R. Jamie Simpson","raw_affiliation_strings":["School of Mathematics, Curtin University, Perth WA 6001, Australia","Curtin University"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Curtin University, Perth WA 6001, Australia","institution_ids":["https://openalex.org/I205640436"]},{"raw_affiliation_string":"Curtin University","institution_ids":["https://openalex.org/I205640436"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061322084"],"corresponding_institution_ids":["https://openalex.org/I53964585"],"apc_list":null,"apc_paid":null,"fwci":0.565,"has_fulltext":true,"cited_by_count":65,"citation_normalized_percentile":{"value":0.71980028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"2","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/substring","display_name":"Substring","score":0.9505099058151245},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8540486693382263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7814078330993652},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.7227557897567749},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.6530804634094238},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5964593291282654},{"id":"https://openalex.org/keywords/pseudorandom-binary-sequence","display_name":"Pseudorandom binary sequence","score":0.4393869638442993},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1351826786994934},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09003892540931702},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.07788178324699402},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.050462037324905396},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.04160892963409424}],"concepts":[{"id":"https://openalex.org/C182407805","wikidata":"https://www.wikidata.org/wiki/Q2626534","display_name":"Substring","level":3,"score":0.9505099058151245},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8540486693382263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7814078330993652},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7227557897567749},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.6530804634094238},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5964593291282654},{"id":"https://openalex.org/C128040838","wikidata":"https://www.wikidata.org/wiki/Q1810628","display_name":"Pseudorandom binary sequence","level":3,"score":0.4393869638442993},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1351826786994934},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09003892540931702},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.07788178324699402},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.050462037324905396},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.04160892963409424},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1196","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1196","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r2/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.37.9979","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.9979","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.maths.tcd.ie/pub/EMIS/journals/EJC/Volume_2/PostScriptfiles/v2i1r2.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.52.5789","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.5789","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.wisdom.weizmann.ac.il/pub/CSreports/reps94/94-23.ps.Z","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1196","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1196","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r2/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1507366302.pdf","grobid_xml":"https://content.openalex.org/works/W1507366302.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W4123800","https://openalex.org/W102084533","https://openalex.org/W1579103288","https://openalex.org/W1982787058","https://openalex.org/W2011042857","https://openalex.org/W2016879150","https://openalex.org/W2018977081","https://openalex.org/W2069902664","https://openalex.org/W2072919316","https://openalex.org/W2080123161","https://openalex.org/W2090631526","https://openalex.org/W2156169026","https://openalex.org/W4214859805","https://openalex.org/W4295030489"],"related_works":["https://openalex.org/W1505605100","https://openalex.org/W4286787697","https://openalex.org/W3043769852","https://openalex.org/W3210979406","https://openalex.org/W4308670360","https://openalex.org/W2950721324","https://openalex.org/W2051304374","https://openalex.org/W4291327800","https://openalex.org/W4230921427","https://openalex.org/W152351265"],"abstract_inverted_index":{"Let":[0],"$g(n)$":[1],"be":[2],"the":[3,34],"length":[4],"of":[5],"a":[6,25,40],"longest":[7],"binary":[8],"string":[9],"containing":[10],"at":[11],"most":[12],"$n$":[13],"distinct":[14],"squares":[15],"(two":[16],"identical":[17],"adjacent":[18],"substrings).":[19],"Then":[20],"$g(0)=3$":[21],"(010":[22],"is":[23],"such":[24],"string),":[26],"$g(1)=7$":[27],"(0001000)":[28],"and":[29],"$g(2)=18$":[30],"(010011000111001101).":[31],"How":[32],"does":[33],"sequence":[35],"$\\{g(n)\\}$":[36],"behave?":[37],"We":[38],"give":[39],"complete":[41],"answer.":[42]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}