{"id":"https://openalex.org/W2093873753","doi":"https://doi.org/10.1137/s089548019528143x","title":"A Gray Code for Necklaces of Fixed Density","display_name":"A Gray Code for Necklaces of Fixed Density","publication_year":1996,"publication_date":"1996-11-01","ids":{"openalex":"https://openalex.org/W2093873753","doi":"https://doi.org/10.1137/s089548019528143x","mag":"2093873753"},"language":"en","primary_location":{"id":"doi:10.1137/s089548019528143x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s089548019528143x","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5076210940","display_name":"Terry Min Yih Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Terry Min Yih Wang","raw_affiliation_strings":["North Carolina State University,"],"affiliations":[{"raw_affiliation_string":"North Carolina State University,","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029085327","display_name":"Carla D. Savage","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carla D. Savage","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076210940"],"corresponding_institution_ids":["https://openalex.org/I137902535"],"apc_list":null,"apc_paid":null,"fwci":2.2089,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.89747656,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"9","issue":"4","first_page":"654","last_page":"673"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9995999932289124,"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":0.9995999932289124,"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":0.998199999332428,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/necklace","display_name":"Necklace","score":0.9433072209358215},{"id":"https://openalex.org/keywords/gray-code","display_name":"Gray code","score":0.783411979675293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.744072675704956},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7360575795173645},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6038143634796143},{"id":"https://openalex.org/keywords/equivalence-class","display_name":"Equivalence class (music)","score":0.5807777047157288},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5284870862960815},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4319709539413452},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.41811490058898926},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4149157404899597},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30055052042007446},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1895357370376587},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14309877157211304},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10233160853385925},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.06322020292282104}],"concepts":[{"id":"https://openalex.org/C2779511736","wikidata":"https://www.wikidata.org/wiki/Q2983383","display_name":"Necklace","level":2,"score":0.9433072209358215},{"id":"https://openalex.org/C129861397","wikidata":"https://www.wikidata.org/wiki/Q332772","display_name":"Gray code","level":2,"score":0.783411979675293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.744072675704956},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7360575795173645},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6038143634796143},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.5807777047157288},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5284870862960815},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4319709539413452},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.41811490058898926},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4149157404899597},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30055052042007446},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1895357370376587},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14309877157211304},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10233160853385925},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.06322020292282104},{"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:10.1137/s089548019528143x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s089548019528143x","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1968708670","https://openalex.org/W1971619037","https://openalex.org/W1971930515","https://openalex.org/W1976395511","https://openalex.org/W1979021998","https://openalex.org/W1983094380","https://openalex.org/W1985733916","https://openalex.org/W1988388271","https://openalex.org/W1989190970","https://openalex.org/W1989216018","https://openalex.org/W1993749868","https://openalex.org/W2012554077","https://openalex.org/W2019778981","https://openalex.org/W2024475703","https://openalex.org/W2050684277","https://openalex.org/W2052085947","https://openalex.org/W2056239531","https://openalex.org/W2066570077","https://openalex.org/W2083867640","https://openalex.org/W2091923122","https://openalex.org/W2093599904","https://openalex.org/W2159338688","https://openalex.org/W2167137513","https://openalex.org/W2294305355","https://openalex.org/W2913978532","https://openalex.org/W4232038591","https://openalex.org/W4300188702"],"related_works":["https://openalex.org/W2111298487","https://openalex.org/W2382232876","https://openalex.org/W2093873753","https://openalex.org/W2182642161","https://openalex.org/W2888427992","https://openalex.org/W4255196547","https://openalex.org/W2358659170","https://openalex.org/W146502352","https://openalex.org/W2055587080","https://openalex.org/W2379751811"],"abstract_inverted_index":{"A":[0],"necklace":[1,31],"is":[2,32,68,83,94],"an":[3],"equivalence":[4,41],"class":[5,42],"of":[6,20,61,75,90],"binary":[7,77],"strings":[8],"under":[9],"rotation.":[10],"In":[11],"this":[12,98],"paper,":[13],"we":[14],"present":[15],"a":[16,37],"Gray":[17],"code":[18],"listing":[19],"all":[21],"n-bit":[22,76],"necklaces":[23,78,89],"with":[24,79],"d":[25,80],"ones":[26],"so":[27],"that":[28],"(i)":[29],"each":[30],"listed":[33],"exactly":[34],"once":[35],"by":[36,58],"representative":[38],"from":[39],"its":[40],"and":[43,50],"(ii)":[44],"successive":[45],"representatives,":[46],"including":[47],"the":[48,51,54,59,73,84],"last":[49],"first":[52,85],"in":[53],"list,":[55],"differ":[56],"only":[57],"transposition":[60],"two":[62],"bits.":[63],"The":[64],"total":[65],"time":[66,99],"required":[67],"${\\text{O}}(nN(n,d))$,":[69],"where":[70],"$N(n,d)$":[71],"denotes":[72],"number":[74],"ones.":[81],"This":[82],"algorithm":[86],"for":[87],"generating":[88],"fixed":[91],"density":[92],"which":[93],"known":[95],"to":[96],"achieve":[97],"bound.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}