{"id":"https://openalex.org/W2046448824","doi":"https://doi.org/10.1137/0207039","title":"Ranking and Listing Algorithms for <i>k</i>-Ary Trees","display_name":"Ranking and Listing Algorithms for <i>k</i>-Ary Trees","publication_year":1978,"publication_date":"1978-11-01","ids":{"openalex":"https://openalex.org/W2046448824","doi":"https://doi.org/10.1137/0207039","mag":"2046448824"},"language":"en","primary_location":{"id":"doi:10.1137/0207039","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0207039","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5047292190","display_name":"Anthony E. Trojanowski","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anthony E. Trojanowski","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5047292190"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0336,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.87007299,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"7","issue":"4","first_page":"492","last_page":"509"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9933000206947327,"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/T11567","display_name":"semigroups and automata theory","score":0.9925000071525574,"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/lexicographical-order","display_name":"Lexicographical order","score":0.8144376277923584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7866724729537964},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7486984133720398},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5976870059967041},{"id":"https://openalex.org/keywords/listing","display_name":"Listing (finance)","score":0.532267689704895},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5099130868911743},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.49174025654792786},{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.4867520332336426},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.48261532187461853},{"id":"https://openalex.org/keywords/weight-balanced-tree","display_name":"Weight-balanced tree","score":0.47870495915412903},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.46290597319602966},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.4550441801548004},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4453260004520416},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4330441951751709},{"id":"https://openalex.org/keywords/binary-search-tree","display_name":"Binary search tree","score":0.2173396646976471},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.15904882550239563},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09800657629966736},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08059796690940857}],"concepts":[{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.8144376277923584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7866724729537964},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7486984133720398},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5976870059967041},{"id":"https://openalex.org/C2779820595","wikidata":"https://www.wikidata.org/wiki/Q798505","display_name":"Listing (finance)","level":2,"score":0.532267689704895},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5099130868911743},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.49174025654792786},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.4867520332336426},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.48261532187461853},{"id":"https://openalex.org/C57900377","wikidata":"https://www.wikidata.org/wiki/Q7979855","display_name":"Weight-balanced tree","level":4,"score":0.47870495915412903},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.46290597319602966},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.4550441801548004},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4453260004520416},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4330441951751709},{"id":"https://openalex.org/C91154448","wikidata":"https://www.wikidata.org/wiki/Q623818","display_name":"Binary search tree","level":3,"score":0.2173396646976471},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.15904882550239563},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09800657629966736},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08059796690940857},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0207039","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0207039","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W195906706","https://openalex.org/W1655990431","https://openalex.org/W1974139773","https://openalex.org/W2027775221","https://openalex.org/W2039339864","https://openalex.org/W2076553474","https://openalex.org/W2157599914","https://openalex.org/W3016176378","https://openalex.org/W4241645849"],"related_works":["https://openalex.org/W2024600207","https://openalex.org/W1587332544","https://openalex.org/W2113387211","https://openalex.org/W2473415529","https://openalex.org/W1926319713","https://openalex.org/W2404891737","https://openalex.org/W1977595606","https://openalex.org/W379674649","https://openalex.org/W2061243524","https://openalex.org/W2461928885"],"abstract_inverted_index":{"The":[0,82,113],"problem":[1,114],"of":[2,53,75,84,93,104,110,115,136],"ranking":[3],"a":[4,18,73,108],"finite":[5],"set":[6,52,74],"X":[7,22,49],"may":[8],"be":[9],"defined":[10],"as":[11],"follows:":[12],"if":[13],"$|X|":[14],"=":[15],"N$,":[16],"define":[17],"linear":[19,66,132],"order":[20,26,67,71],"on":[21,56,72,120],"and":[23,38,96],"find":[24],"the":[25,51,65,69,80,134],"isomorphism":[27],"$\\varphi":[28,41,94,97],":X":[29],"\\to":[30],"\\{":[31],"0,1,":[32],"\\cdots":[33],",N":[34],"-":[35,43,99],"1\\}":[36],"$,":[37],"its":[39],"inverse":[40],"^{":[42,98],"1}":[44,100],"$.":[45,101],"In":[46],"this":[47,105],"paper,":[48],"is":[50,68,107,123,131,139],"k-ary":[54,85,118],"trees":[55,86,119,138],"n":[57,121],"vertices,":[58],"$k":[59],"\\geqq":[60,63],"2$,":[61],"$n":[62],"0$;":[64],"lexicographic":[70],"permutations":[76,88],"used":[77],"to":[78,90],"represent":[79],"trees.":[81],"representation":[83],"by":[87],"leads":[89],"efficient":[91],"computation":[92],"$":[95],"One":[102],"result":[103],"investigation":[106],"generalization":[109],"binomial":[111],"coefficients.":[112],"listing":[116],"all":[117],"vertices":[122],"also":[124],"addressed;":[125],"an":[126],"algorithm":[127],"which,":[128],"excluding":[129],"input-output,":[130],"in":[133],"number":[135],"such":[137],"presented.":[140]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"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"}