{"id":"https://openalex.org/W2073316125","doi":"https://doi.org/10.1137/06066326x","title":"Labeled Partitions and the <i>q</i>-Derangement Numbers","display_name":"Labeled Partitions and the <i>q</i>-Derangement Numbers","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2073316125","doi":"https://doi.org/10.1137/06066326x","mag":"2073316125"},"language":"en","primary_location":{"id":"doi:10.1137/06066326x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06066326x","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/A5006776804","display_name":"William Y. C. Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"William Y. C. Chen","raw_affiliation_strings":["chen@nankai.edu.cn and xudeheng@eyou.com#TAB#"],"affiliations":[{"raw_affiliation_string":"chen@nankai.edu.cn and xudeheng@eyou.com#TAB#","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043273571","display_name":"Deheng Xu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Deheng Xu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006776804"],"corresponding_institution_ids":["https://openalex.org/I205237279"],"apc_list":null,"apc_paid":null,"fwci":3.2501,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.91302056,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"3","first_page":"1099","last_page":"1104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9979000091552734,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9570000171661377,"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/derangement","display_name":"Derangement","score":0.9790477752685547},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.875516414642334},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7941601276397705},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7704710364341736},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.7467407584190369},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5152852535247803},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42133674025535583},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4138070046901703}],"concepts":[{"id":"https://openalex.org/C38298161","wikidata":"https://www.wikidata.org/wiki/Q1207920","display_name":"Derangement","level":2,"score":0.9790477752685547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.875516414642334},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7941601276397705},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7704710364341736},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7467407584190369},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5152852535247803},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42133674025535583},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4138070046901703},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/06066326x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06066326x","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":[{"score":0.5400000214576721,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1987721903","https://openalex.org/W1995626171","https://openalex.org/W2006479146","https://openalex.org/W2011087200","https://openalex.org/W2046894670","https://openalex.org/W2074707306","https://openalex.org/W2077309624","https://openalex.org/W2125838758","https://openalex.org/W2752853835","https://openalex.org/W2914659449","https://openalex.org/W3027900649"],"related_works":["https://openalex.org/W4318908287","https://openalex.org/W4298457394","https://openalex.org/W2769202988","https://openalex.org/W2950642020","https://openalex.org/W1721535522","https://openalex.org/W4386833582","https://openalex.org/W1596411003","https://openalex.org/W4301839635","https://openalex.org/W2338752714","https://openalex.org/W3004838398"],"abstract_inverted_index":{"Inspired":[0],"by":[1],"MacMahon's":[2],"original":[3],"proof":[4],"of":[5,12,22,27,47,61,84],"his":[6,23],"celebrated":[7],"theorem":[8,37],"on":[9,72,87],"the":[10,13,45,65,69,88],"distribution":[11],"major":[14,70],"index":[15,71],"over":[16],"permutations,":[17],"we":[18,33],"give":[19],"a":[20,35,48,59,81],"reformulation":[21,60],"argument":[24],"in":[25,77],"terms":[26],"labeled":[28,39],"partitions.":[29],"In":[30],"this":[31],"framework,":[32],"establish":[34],"decomposition":[36,46,57],"for":[38],"partitions":[40],"which":[41,74],"is":[42],"analogous":[43],"to":[44,79],"permutation":[49],"into":[50],"derangement":[51,66],"points":[52],"and":[53,68],"fixed":[54],"points.":[55],"This":[56],"implies":[58],"Wachs's":[62],"formula":[63,86],"concerning":[64],"parts":[67],"permutations":[73],"was":[75],"derived":[76],"order":[78],"present":[80],"bijective":[82],"treatment":[83],"Gessel's":[85],"q-derangement":[89],"numbers.":[90]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}