{"id":"https://openalex.org/W2961176507","doi":"https://doi.org/10.1109/tit.2019.2928292","title":"A Successor Rule Framework for Constructing $k$ -Ary de Bruijn Sequences and Universal Cycles","display_name":"A Successor Rule Framework for Constructing $k$ -Ary de Bruijn Sequences and Universal Cycles","publication_year":2019,"publication_date":"2019-07-16","ids":{"openalex":"https://openalex.org/W2961176507","doi":"https://doi.org/10.1109/tit.2019.2928292","mag":"2961176507"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2019.2928292","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2928292","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020810376","display_name":"Daniel Gabri\u0107","orcid":"https://orcid.org/0000-0001-9707-0803"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"D. Gabric","raw_affiliation_strings":["University of Waterloo, Waterloo, Canada"],"raw_orcid":"https://orcid.org/0000-0001-9707-0803","affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","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":"J. Sawada","raw_affiliation_strings":["School of Computer Science, University of Guelph, Guelph, Canada"],"raw_orcid":"https://orcid.org/0000-0001-7364-2993","affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Guelph, Guelph, Canada","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/I22675022","display_name":"Williams College","ror":"https://ror.org/04avkmd49","country_code":"US","type":"education","lineage":["https://openalex.org/I22675022"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Williams","raw_affiliation_strings":["Department of Computer Science, Williams College, Williamstown, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Williams College, Williamstown, MA, USA","institution_ids":["https://openalex.org/I22675022"]}]},{"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/I4210116376","display_name":"SUNY Korea","ror":"https://ror.org/02d07gm56","country_code":"KR","type":"education","lineage":["https://openalex.org/I4210116376"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"D. Wong","raw_affiliation_strings":["Department of Computer Science, SUNY Korea, Incheon, South Korea"],"raw_orcid":"https://orcid.org/0000-0002-6242-164X","affiliations":[{"raw_affiliation_string":"Department of Computer Science, SUNY Korea, Incheon, South Korea","institution_ids":["https://openalex.org/I4210116376"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.965,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.93021558,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"66","issue":"1","first_page":"679","last_page":"687"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9951000213623047,"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":0.9937000274658203,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/de-bruijn-sequence","display_name":"De Bruijn sequence","score":0.9283417463302612},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5493277907371521},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5236684679985046},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4852330684661865},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4739304184913635},{"id":"https://openalex.org/keywords/successor-cardinal","display_name":"Successor cardinal","score":0.45151758193969727},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.4487426280975342},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4285220503807068},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.42117446660995483},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.41113072633743286},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3904259204864502},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3253040909767151},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3244272768497467},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3040096163749695},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17579495906829834},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1517098844051361}],"concepts":[{"id":"https://openalex.org/C170320093","wikidata":"https://www.wikidata.org/wiki/Q1953457","display_name":"De Bruijn sequence","level":2,"score":0.9283417463302612},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5493277907371521},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5236684679985046},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4852330684661865},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4739304184913635},{"id":"https://openalex.org/C75306776","wikidata":"https://www.wikidata.org/wiki/Q7632662","display_name":"Successor cardinal","level":2,"score":0.45151758193969727},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4487426280975342},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4285220503807068},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.42117446660995483},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.41113072633743286},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3904259204864502},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3253040909767151},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3244272768497467},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3040096163749695},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17579495906829834},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1517098844051361},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2019.2928292","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2928292","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1602689873","https://openalex.org/W1745342855","https://openalex.org/W1965627014","https://openalex.org/W1966042291","https://openalex.org/W1973343935","https://openalex.org/W1976395511","https://openalex.org/W1990570130","https://openalex.org/W1995300673","https://openalex.org/W2011693214","https://openalex.org/W2012661148","https://openalex.org/W2021003109","https://openalex.org/W2023800056","https://openalex.org/W2058219874","https://openalex.org/W2065636918","https://openalex.org/W2075879870","https://openalex.org/W2076568250","https://openalex.org/W2095842254","https://openalex.org/W2100731258","https://openalex.org/W2200124835","https://openalex.org/W2489207806","https://openalex.org/W2551168410","https://openalex.org/W2799851485","https://openalex.org/W2885945836"],"related_works":["https://openalex.org/W2473542051","https://openalex.org/W3123320268","https://openalex.org/W3198016531","https://openalex.org/W2994519609","https://openalex.org/W2726593096","https://openalex.org/W2054269721","https://openalex.org/W127787461","https://openalex.org/W2039773446","https://openalex.org/W1998517951","https://openalex.org/W2126473010"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,58],"simple":[3],"framework":[4,26,88],"for":[5,105,138,153],"constructing":[6],"<inline-formula":[7,106,116,128],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[8,107,117,129],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[9,108,118,130],"<tex-math":[10,109,119,131],"notation=\"LaTeX\">$k$":[11,110],"</tex-math></inline-formula>":[12,111,121,133],"-ary":[13,112],"de":[14,43,77],"Bruijn":[15,44,78],"sequences,":[16],"and":[17,53,93,134],"more":[18],"generally,":[19],"universal":[20,103,136,150],"cycles,":[21],"via":[22],"successor":[23],"rules.":[24],"The":[25,87],"is":[27,54,62,89,124],"based":[28,47,80],"on":[29,48,81],"the":[30,49,64,95,148],"often":[31],"used":[32],"method":[33],"of":[34,66,97,114],"joining":[35],"disjoint":[36],"cycles.":[37],"It":[38,140],"generalizes":[39,71],"several":[40],"previously":[41],"known":[42],"sequence":[45],"constructions":[46,152],"pure":[50],"cycling":[51],"register":[52],"applied":[55,90,145],"to":[56,74,91,99,146],"derive":[57,92],"new":[59],"construction":[60],"that":[61],"perhaps":[63],"simplest":[65],"all":[67],"successors.":[68],"Furthermore,":[69],"it":[70],"an":[72],"algorithm":[73],"construct":[75,101],"binary":[76],"sequences":[79],"any":[82],"arbitrary":[83],"nonsingular":[84],"feedback":[85],"function.":[86],"prove":[94],"correctness":[96],"successors":[98],"efficiently":[100],"1)":[102],"cycles":[104,137],"strings":[113],"length":[115],"notation=\"LaTeX\">$n$":[120],"whose":[122],"weight":[123],"bounded":[125],"by":[126],"some":[127],"notation=\"LaTeX\">$w$":[132],"2)":[135],"permutations.":[139],"has":[141],"also":[142],"been":[143],"subsequently":[144],"find":[147],"first":[149],"cycle":[151],"weak":[154],"orders.":[155]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
