{"id":"https://openalex.org/W1910352922","doi":"https://doi.org/10.37236/1241","title":"Gray Codes for A-Free Strings","display_name":"Gray Codes for A-Free Strings","publication_year":1996,"publication_date":"1996-02-14","ids":{"openalex":"https://openalex.org/W1910352922","doi":"https://doi.org/10.37236/1241","mag":"1910352922"},"language":"en","primary_location":{"id":"doi:10.37236/1241","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1241","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i1r17/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/v3i1r17/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069660363","display_name":"Matthew B. Squire","orcid":null},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]},{"id":"https://openalex.org/I1309191912","display_name":"Research Triangle Park Foundation","ror":"https://ror.org/03eqttr49","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1309191912"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthew B. Squire","raw_affiliation_strings":["IBM Corporation Dept NFVA/Bldg 664 P.O. Box 12195 Research Triangle Park, NC 27709","IBM, ,"],"affiliations":[{"raw_affiliation_string":"IBM Corporation Dept NFVA/Bldg 664 P.O. Box 12195 Research Triangle Park, NC 27709","institution_ids":["https://openalex.org/I1309191912"]},{"raw_affiliation_string":"IBM, ,","institution_ids":["https://openalex.org/I1341412227"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069660363"],"corresponding_institution_ids":["https://openalex.org/I1309191912","https://openalex.org/I1341412227"],"apc_list":null,"apc_paid":null,"fwci":1.1386,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.81867248,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"3","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":0.9998000264167786,"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":0.9998000264167786,"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/T11567","display_name":"semigroups and automata theory","score":0.9991000294685364,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7568269968032837},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6993739604949951},{"id":"https://openalex.org/keywords/substring","display_name":"Substring","score":0.6786013841629028},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.6080243587493896},{"id":"https://openalex.org/keywords/gray-code","display_name":"Gray code","score":0.5689552426338196},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4512452781200409},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.4483918249607086},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20257717370986938},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16849026083946228},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11759120225906372},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.05708271265029907},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05652680993080139}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7568269968032837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6993739604949951},{"id":"https://openalex.org/C182407805","wikidata":"https://www.wikidata.org/wiki/Q2626534","display_name":"Substring","level":3,"score":0.6786013841629028},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.6080243587493896},{"id":"https://openalex.org/C129861397","wikidata":"https://www.wikidata.org/wiki/Q332772","display_name":"Gray code","level":2,"score":0.5689552426338196},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4512452781200409},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.4483918249607086},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20257717370986938},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16849026083946228},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11759120225906372},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.05708271265029907},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05652680993080139},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1241","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1241","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i1r17/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"}],"best_oa_location":{"id":"doi:10.37236/1241","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1241","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i1r17/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":[{"id":"https://openalex.org/G1630494089","display_name":"Gray Codes, Efficient Generation, and Structure in          Combinatorial Families","funder_award_id":"9302505","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1910352922.pdf","grobid_xml":"https://content.openalex.org/works/W1910352922.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W104215891","https://openalex.org/W1967824225","https://openalex.org/W1984910974","https://openalex.org/W2005315460","https://openalex.org/W2014147471","https://openalex.org/W2015569722","https://openalex.org/W2019198417","https://openalex.org/W2152954365","https://openalex.org/W2911361414","https://openalex.org/W4205562629","https://openalex.org/W4291474784"],"related_works":["https://openalex.org/W1583922594","https://openalex.org/W1542422837","https://openalex.org/W1974038726","https://openalex.org/W2998448420","https://openalex.org/W1598224733","https://openalex.org/W4304731099","https://openalex.org/W4280502676","https://openalex.org/W2000769876","https://openalex.org/W204227468","https://openalex.org/W2255137899"],"abstract_inverted_index":{"For":[0],"any":[1],"$q":[2],"\\geq":[3,91,178],"2$,":[4],"let":[5],"$\\Sigma_{q}=\\{0,\\ldots,q\\!-\\!1\\}$,":[6],"and":[7,58,83,119],"fix":[8],"a":[9,31,66,69,93,106,165],"string":[10],"$A$":[11,29,84,151],"over":[12],"$\\Sigma_{q}$.":[13],"The":[14],"$A$-free":[15,44,74,98,133,170],"strings":[16,22,45,52,75,99,134,171],"of":[17,41,46,76,100,117,122,135,157,172],"length":[18,47,77,101,136,173],"$n$":[19,48,102,174],"are":[20],"the":[21,39,43,73,97,132,145,169],"in":[23,54,62],"$\\Sigma_{q}^n$":[24],"which":[25,153],"do":[26,160],"not":[27,161],"contain":[28],"as":[30],"contiguous":[32],"substring.":[33],"In":[34],"this":[35],"paper,":[36],"we":[37,142,163],"investigate":[38],"possibility":[40],"listing":[42,67],"so":[49],"that":[50,63],"successive":[51],"differ":[53],"only":[55],"one":[56],"position,":[57],"by":[59,105],"$\\pm":[60],"1$":[61],"position.":[64],"Such":[65],"is":[68,103,140],"Gray":[70,94,166],"code":[71,95,167],"for":[72,87,96,149,152,168,175],"$n$.":[78,137],"We":[79],"identify":[80],"those":[81,116,150],"$q$":[82,139],"such":[85],"that,":[86],"infinitely":[88],"many":[89],"$n":[90,177],"0$,":[92],"prohibited":[104],"parity":[107,110,158],"problem.":[108],"Our":[109],"argument":[111],"uses":[112],"techniques":[113],"similar":[114],"to":[115],"Guibas":[118],"Odlyzko":[120],"(Journal":[121],"Combinatorial":[123],"Theory":[124],"A":[125],"30":[126],"(1981)":[127],"pp.":[128],"183\u2013208)":[129],"who":[130],"enumerated":[131],"When":[138],"even,":[141],"also":[143],"give":[144],"complementary":[146],"positive":[147],"result:":[148],"an":[154],"infinite":[155],"number":[156],"problems":[159],"exist,":[162],"construct":[164],"all":[176],"0$.":[179]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
