{"id":"https://openalex.org/W2290281988","doi":"https://doi.org/10.37236/5517","title":"Generalizing the Classic Greedy and Necklace Constructions of de Bruijn Sequences and Universal Cycles","display_name":"Generalizing the Classic Greedy and Necklace Constructions of de Bruijn Sequences and Universal Cycles","publication_year":2016,"publication_date":"2016-02-05","ids":{"openalex":"https://openalex.org/W2290281988","doi":"https://doi.org/10.37236/5517","mag":"2290281988"},"language":"en","primary_location":{"id":"doi:10.37236/5517","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5517","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p24/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p24/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060694274","display_name":"Joe Sawada","orcid":"https://orcid.org/0000-0001-7364-2993"},"institutions":[{"id":"https://openalex.org/I79817857","display_name":"University of Guelph","ror":"https://ror.org/01r7awg59","country_code":"CA","type":"education","lineage":["https://openalex.org/I79817857"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Joe Sawada","raw_affiliation_strings":["University of Guelph"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Guelph","institution_ids":["https://openalex.org/I79817857"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032232670","display_name":"Aaron Williams","orcid":"https://orcid.org/0000-0001-6816-4368"},"institutions":[{"id":"https://openalex.org/I131240579","display_name":"Bard College at Simon's Rock","ror":"https://ror.org/034pcpg38","country_code":"US","type":"education","lineage":["https://openalex.org/I131240579"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aaron Williams","raw_affiliation_strings":["Bard College of Simon's Rock"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bard College of Simon's Rock","institution_ids":["https://openalex.org/I131240579"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059002802","display_name":"Dennis Wong","orcid":"https://orcid.org/0000-0002-6242-164X"},"institutions":[{"id":"https://openalex.org/I11123151","display_name":"Northwest Missouri State University","ror":"https://ror.org/05maved80","country_code":"US","type":"education","lineage":["https://openalex.org/I11123151"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dennis Wong","raw_affiliation_strings":["Northwest Missouri State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Northwest Missouri State University","institution_ids":["https://openalex.org/I11123151"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7324,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.88555744,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","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":0.9997000098228455,"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":0.9997000098228455,"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/T11130","display_name":"Coding theory and cryptography","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/necklace","display_name":"Necklace","score":0.9376717805862427},{"id":"https://openalex.org/keywords/concatenation","display_name":"Concatenation (mathematics)","score":0.7641686201095581},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7481789588928223},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7179326415061951},{"id":"https://openalex.org/keywords/de-bruijn-sequence","display_name":"De Bruijn sequence","score":0.7100769281387329},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.6365567445755005},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.507396399974823},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.49232304096221924},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4867737293243408},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.48287585377693176},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.4812057316303253},{"id":"https://openalex.org/keywords/suffix","display_name":"Suffix","score":0.4658803343772888},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.46393993496894836},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.44111761450767517},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43946918845176697},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14339980483055115}],"concepts":[{"id":"https://openalex.org/C2779511736","wikidata":"https://www.wikidata.org/wiki/Q2983383","display_name":"Necklace","level":2,"score":0.9376717805862427},{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.7641686201095581},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7481789588928223},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7179326415061951},{"id":"https://openalex.org/C170320093","wikidata":"https://www.wikidata.org/wiki/Q1953457","display_name":"De Bruijn sequence","level":2,"score":0.7100769281387329},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.6365567445755005},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.507396399974823},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.49232304096221924},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4867737293243408},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48287585377693176},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4812057316303253},{"id":"https://openalex.org/C2779804580","wikidata":"https://www.wikidata.org/wiki/Q102047","display_name":"Suffix","level":2,"score":0.4658803343772888},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.46393993496894836},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.44111761450767517},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43946918845176697},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14339980483055115},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":1,"locations":[{"id":"doi:10.37236/5517","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5517","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p24/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:10.37236/5517","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5517","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p24/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2290281988.pdf","grobid_xml":"https://content.openalex.org/works/W2290281988.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1614349107","https://openalex.org/W1976395511","https://openalex.org/W1988388271","https://openalex.org/W1997415583","https://openalex.org/W2006913132","https://openalex.org/W2012661148","https://openalex.org/W2015696676","https://openalex.org/W2022465678","https://openalex.org/W2023800056","https://openalex.org/W2029948740","https://openalex.org/W2032366410","https://openalex.org/W2033624808","https://openalex.org/W2035511639","https://openalex.org/W2045924045","https://openalex.org/W2066342920","https://openalex.org/W2069636145","https://openalex.org/W2081569145","https://openalex.org/W2085157194","https://openalex.org/W2095842254","https://openalex.org/W2100731258","https://openalex.org/W2105321516","https://openalex.org/W2110188594","https://openalex.org/W2119711807","https://openalex.org/W2141324117","https://openalex.org/W2141731854","https://openalex.org/W2155777273","https://openalex.org/W2329095262","https://openalex.org/W2541501618","https://openalex.org/W2592570088","https://openalex.org/W2752853835","https://openalex.org/W2913978532","https://openalex.org/W2949574883","https://openalex.org/W2963757710","https://openalex.org/W2998737478","https://openalex.org/W3020856174","https://openalex.org/W4248882684","https://openalex.org/W6649800611","https://openalex.org/W6656488746","https://openalex.org/W6661609531","https://openalex.org/W6671703357","https://openalex.org/W6674489828","https://openalex.org/W6682835449","https://openalex.org/W6758769178","https://openalex.org/W6764004426","https://openalex.org/W6808507831"],"related_works":["https://openalex.org/W3021903883","https://openalex.org/W4231369123","https://openalex.org/W2946754585","https://openalex.org/W3008198343","https://openalex.org/W2387943738","https://openalex.org/W4386185002","https://openalex.org/W2586556622","https://openalex.org/W2799851485","https://openalex.org/W4296118933","https://openalex.org/W2953160532"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,106,117,123],"class":[3,127],"of":[4,43,58,67,73,141],"languages":[5,41],"that":[6,50,92],"have":[7],"an":[8],"interesting":[9],"property:":[10],"For":[11],"each":[12],"language":[13],"$\\mathbf{L}$":[14],"in":[15],"the":[16,19,24,33],"class,":[17],"both":[18,132],"classic":[20,25],"greedy":[21],"algorithm":[22,31],"and":[23,120,134,136],"Lyndon":[26],"word":[27],"(or":[28],"necklace)":[29],"concatenation":[30],"provide":[32],"lexicographically":[34],"smallest":[35],"universal":[36,82],"cycle":[37],"for":[38,105,116],"$\\mathbf{L}$.":[39],"The":[40],"consist":[42],"length":[44,68],"$n$":[45],"strings":[46,78,91,98,109,121],"over":[47],"$\\{1,2,\\ldots":[48],",k\\}$":[49],"are":[51,84],"closed":[52,62,130],"under":[53,63,131],"rotation":[54],"with":[55,99,110],"their":[56],"subset":[57],"necklaces":[59],"also":[60,129],"being":[61],"replacing":[64],"any":[65],"suffix":[66],"$i$":[69,71],"by":[70],"copies":[72],"$k$.":[74],"Examples":[75],"include":[76],"all":[77],"(in":[79],"which":[80],"case":[81],"cycles":[83],"commonly":[85],"known":[86],"as":[87],"de":[88],"Bruijn":[89],"sequences),":[90],"sum":[93],"to":[94],"at":[95,100,111],"least":[96],"$s$,":[97],"most":[101,112],"$d$":[102,113],"cyclic":[103,114],"descents":[104],"fixed":[107,118],"$d>0$,":[108,119],"decrements":[115],"avoiding":[122],"given":[124],"period.":[125],"Our":[126],"is":[128],"union":[133],"intersection,":[135],"our":[137],"results":[138,140],"generalize":[139],"several":[142],"previous":[143],"papers.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}