{"id":"https://openalex.org/W2093386412","doi":"https://doi.org/10.1137/0208006","title":"Generating Trees and Other Combinatorial Objects Lexicographically","display_name":"Generating Trees and Other Combinatorial Objects Lexicographically","publication_year":1979,"publication_date":"1979-02-01","ids":{"openalex":"https://openalex.org/W2093386412","doi":"https://doi.org/10.1137/0208006","mag":"2093386412"},"language":"en","primary_location":{"id":"doi:10.1137/0208006","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0208006","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/A5009919512","display_name":"Shmuel Zaks","orcid":"https://orcid.org/0000-0001-5637-4923"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Zaks","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036610989","display_name":"Dana Richards","orcid":"https://orcid.org/0000-0002-7260-4394"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. Richards","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.855,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.94961832,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"8","issue":"1","first_page":"73","last_page":"81"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9973999857902527,"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":0.9973999857902527,"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/T11106","display_name":"Data Management and Algorithms","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9724000096321106,"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":0.8863896131515503},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8382153511047363},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.7384456992149353},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.699163556098938},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.46791890263557434},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41018396615982056},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07531514763832092}],"concepts":[{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.8863896131515503},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8382153511047363},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.7384456992149353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.699163556098938},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.46791890263557434},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41018396615982056},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07531514763832092},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0208006","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0208006","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":11,"referenced_works":["https://openalex.org/W47591876","https://openalex.org/W195906706","https://openalex.org/W1964195795","https://openalex.org/W1974139773","https://openalex.org/W2000019910","https://openalex.org/W2034011690","https://openalex.org/W2039339864","https://openalex.org/W2046448824","https://openalex.org/W2050034390","https://openalex.org/W2075970910","https://openalex.org/W4241007652"],"related_works":["https://openalex.org/W1985455246","https://openalex.org/W2369655046","https://openalex.org/W1993634787","https://openalex.org/W3125614403","https://openalex.org/W2019467317","https://openalex.org/W2476923378","https://openalex.org/W1585519779","https://openalex.org/W1965515989","https://openalex.org/W2803221307","https://openalex.org/W4376167435"],"abstract_inverted_index":{"We":[0],"show":[1],"a":[2],"one-to-one":[3],"correspondence":[4],"between":[5],"all":[6,42],"the":[7,43,47,53,63,70,87,93],"ordered":[8,88],"trees":[9],"that":[10],"have":[11],"$n_0":[12,33],"+":[13,49],"1$":[14],"leaves":[15],"and":[16,41,92,95],"$n_i":[17],"$":[18,23],"internal":[19],"nodes":[20],"with":[21],"$k_i":[22],"sons":[24],"each,":[25],"for":[26,81],"$i":[27],"=":[28,34,73],"1,":[29],"\\cdots":[30,58],",t$,":[31],"(hence":[32],"\\sum_1^t":[35,74],"(k_i":[36,75],"-":[37,76],"1)":[38,77],"n_i":[39],"$)":[40],"lattice":[44],"paths":[45,84],"in":[46],"$(t":[48],"1)$-dimensional":[50],"space,":[51],"from":[52],"point":[54],"$(n_0":[55],",n_1":[56],",":[57,59],"n_t":[60],")$":[61],"to":[62],"origin,":[64],"which":[65],"do":[66],"not":[67],"go":[68],"below":[69],"hyperplane":[71],"$x_0":[72],"x_i":[78],"$.":[79],"Procedures":[80],"generating":[82],"these":[83],"(and":[85],"thus":[86],"trees)":[89],"are":[90,98],"presented":[91],"ranking":[94],"unranking":[96],"procedures":[97],"derived.":[99]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}