{"id":"https://openalex.org/W4391244910","doi":"https://doi.org/10.4230/lipics.aofa.2024.17","title":"Lexicographic Unranking Algorithms for the Twelvefold Way","display_name":"Lexicographic Unranking Algorithms for the Twelvefold Way","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4391244910","doi":"https://doi.org/10.4230/lipics.aofa.2024.17"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-04411470v1","is_oa":true,"landing_page_url":"https://hal.sorbonne-universite.fr/hal-04411470","pdf_url":"https://hal.sorbonne-universite.fr/hal-04411470/file/CurielGenitrini.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.sorbonne-universite.fr/hal-04411470","raw_type":"info:eu-repo/semantics/preprint"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.sorbonne-universite.fr/hal-04411470/file/CurielGenitrini.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093793095","display_name":"Amaury Curiel","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210159731","display_name":"LIP6","ror":"https://ror.org/05krcen59","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159245","https://openalex.org/I4210159731"]},{"id":"https://openalex.org/I51101395","display_name":"Universit\u00e9 Paris 1 Panth\u00e9on-Sorbonne","ror":"https://ror.org/002t25c44","country_code":"FR","type":"education","lineage":["https://openalex.org/I51101395"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Curiel, Amaury","raw_affiliation_strings":["Sorbonne Universit\u00e9, CNRS, LIP6 - UMR 7606, Paris, France","Algorithmes, Programmes et R\u00e9solution"],"raw_orcid":"https://orcid.org/0009-0008-2416-4137","affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9, CNRS, LIP6 - UMR 7606, Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I51101395","https://openalex.org/I1294671590","https://openalex.org/I4210159731"]},{"raw_affiliation_string":"Algorithmes, Programmes et R\u00e9solution","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088215033","display_name":"Antoine Genitrini","orcid":"https://orcid.org/0000-0002-5480-0236"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210159731","display_name":"LIP6","ror":"https://ror.org/05krcen59","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159245","https://openalex.org/I4210159731"]},{"id":"https://openalex.org/I51101395","display_name":"Universit\u00e9 Paris 1 Panth\u00e9on-Sorbonne","ror":"https://ror.org/002t25c44","country_code":"FR","type":"education","lineage":["https://openalex.org/I51101395"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Genitrini, Antoine","raw_affiliation_strings":["Sorbonne Universit\u00e9, CNRS, LIP6 - UMR 7606, Paris, France","Algorithmes, Programmes et R\u00e9solution"],"raw_orcid":"https://orcid.org/0000-0002-5480-0236","affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9, CNRS, LIP6 - UMR 7606, Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I51101395","https://openalex.org/I1294671590","https://openalex.org/I4210159731"]},{"raw_affiliation_string":"Algorithmes, Programmes et R\u00e9solution","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5093793095"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159731","https://openalex.org/I51101395"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00707188,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10181","display_name":"Natural Language Processing Techniques","score":0.8137000203132629,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.8137000203132629,"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/T13083","display_name":"Advanced Text Analysis Techniques","score":0.809499979019165,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.7724999785423279,"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/lexicographical-order","display_name":"Lexicographical order","score":0.7355583310127258},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6537392139434814},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5123082399368286},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2634263336658478},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13658645749092102}],"concepts":[{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.7355583310127258},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6537392139434814},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5123082399368286},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2634263336658478},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13658645749092102}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:HAL:hal-04411470v1","is_oa":true,"landing_page_url":"https://hal.sorbonne-universite.fr/hal-04411470","pdf_url":"https://hal.sorbonne-universite.fr/hal-04411470/file/CurielGenitrini.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.sorbonne-universite.fr/hal-04411470","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:drops-oai.dagstuhl.de:20452","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.17","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol302-aofa2024/LIPIcs.AofA.2024.17/LIPIcs.AofA.2024.17.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"doi:10.4230/lipics.aofa.2024.17","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.aofa.2024.17","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04411470v1","is_oa":true,"landing_page_url":"https://hal.sorbonne-universite.fr/hal-04411470","pdf_url":"https://hal.sorbonne-universite.fr/hal-04411470/file/CurielGenitrini.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.sorbonne-universite.fr/hal-04411470","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6268741103","display_name":null,"funder_award_id":"0014-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G946709030","display_name":"Parameter ANalysis of certain classes of DAGs","funder_award_id":"ANR-23-CE48-0014","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391244910.pdf","grobid_xml":"https://content.openalex.org/works/W4391244910.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W1993634787","https://openalex.org/W3125614403","https://openalex.org/W2476923378","https://openalex.org/W3100240142","https://openalex.org/W2803221307","https://openalex.org/W4211001408","https://openalex.org/W2903963821","https://openalex.org/W2366147410"],"abstract_inverted_index":{"The":[0,39],"Twelvefold":[1],"Way":[2],"represents":[3],"Rota\u2019s":[4,130],"classification,":[5],"addressing":[6],"the":[7,43,66,76,86,89,92,104,110,114,126,145,162,175,182,187,196,199,214],"most":[8,115],"fundamental":[9],"enumeration":[10],"problems":[11,20,45,146],"and":[12,208],"their":[13],"associated":[14,180],"combinatorial":[15],"counting":[16,40,127],"formulas.":[17],"These":[18],"distinct":[19],"are":[21,46,50],"connected":[22],"to":[23,85,122,140,194],"enumerating":[24],"functions":[25],"defined":[26],"from":[27],"a":[28,206],"set":[29,67,178],"of":[30,68,78,186,216],"elements":[31],"denoted":[32],"by":[33,117],"\ud835\udca9":[34],"into":[35],"another":[36],"one":[37,111,120],"\ud835\udca6.":[38],"solutions":[41,128],"for":[42,129,135,161,177,198],"twelve":[44],"well":[47],"known.":[48],"We":[49],"interested":[51],"in":[52,173],"unranking":[53,151],"algorithms.":[54,170],"Such":[55],"an":[56,61,79],"algorithm":[57,90,197],"is":[58,103,108,113,138],"based":[59,212],"on":[60,65,213],"underlying":[62],"total":[63,87,101],"order":[64,102,123],"structures":[69],"we":[70,156,190,204],"aim":[71,157],"at":[72,158],"constructing.":[73],"By":[74],"taking":[75],"rank":[77],"object,":[80],"i.e.":[81],"its":[82],"number":[83,215],"according":[84],"order,":[88],"outputs":[91],"structure":[93],"itself":[94],"after":[95],"having":[96],"built":[97],"it.":[98],"One":[99],"famous":[100,183],"lexicographic":[105,150],"order:":[106],"it":[107,137],"probably":[109],"that":[112,142,166],"used":[116],"people":[118],"when":[119],"wants":[121],"things.":[124],"While":[125],"classification":[131],"have":[132,147],"been":[133],"known":[134],"years":[136],"interesting":[139],"note":[141],"three":[143,164],"among":[144],"yet":[148],"no":[149],"algorithm.":[152],"In":[153],"this":[154],"paper":[155],"providing":[159],"algorithms":[160],"last":[163],"cases":[165],"remain":[167],"without":[168],"such":[169],"After":[171],"presenting":[172],"detail":[174],"solution":[176],"partitions":[179],"with":[181],"Stirling":[184],"numbers":[185],"second":[188],"kind,":[189],"explicitly":[191],"explain":[192],"how":[193],"adapt":[195],"two":[200],"remaining":[201],"cases.":[202],"Additionally,":[203],"propose":[205],"detailed":[207],"fine-grained":[209],"complexity":[210],"analysis":[211],"bitwise":[217],"arithmetic":[218],"operations.":[219]},"counts_by_year":[],"updated_date":"2026-05-16T08:24:45.110214","created_date":"2025-10-10T00:00:00"}
