{"id":"https://openalex.org/W7127167246","doi":"https://doi.org/10.5070/c65465679","title":"Some enumerative properties of parking functions","display_name":"Some enumerative properties of parking functions","publication_year":2026,"publication_date":"2026-02-02","ids":{"openalex":"https://openalex.org/W7127167246","doi":"https://doi.org/10.5070/c65465679"},"language":null,"primary_location":{"id":"doi:10.5070/c65465679","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65465679","pdf_url":"https://escholarship.org/content/qt9862s2dg/qt9862s2dg.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt9862s2dg/qt9862s2dg.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079674634","display_name":"Richard P. Stanley","orcid":"https://orcid.org/0000-0003-3123-8241"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Richard P. Stanley","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046131816","display_name":"Mei Yin","orcid":"https://orcid.org/0000-0002-3706-9357"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mei Yin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079674634"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28156927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.6679999828338623,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.6679999828338623,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.13600000739097595,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.032499998807907104,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.7638999819755554},{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"Joint probability distribution","score":0.6025000214576721},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.5752000212669373},{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.5631999969482422},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5311999917030334},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5175999999046326},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4975999891757965},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.45910000801086426}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7638999819755554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7129999995231628},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.6025000214576721},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.5752000212669373},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.5631999969482422},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5311999917030334},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5271999835968018},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5175999999046326},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4975999891757965},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.45910000801086426},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44440001249313354},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4375},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.3946000039577484},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.36500000953674316},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C2777427512","wikidata":"https://www.wikidata.org/wiki/Q6501349","display_name":"Parking lot","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C24404364","wikidata":"https://www.wikidata.org/wiki/Q7246846","display_name":"Probabilistic analysis of algorithms","level":3,"score":0.28859999775886536},{"id":"https://openalex.org/C112497148","wikidata":"https://www.wikidata.org/wiki/Q336787","display_name":"Enumerative combinatorics","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C60782215","wikidata":"https://www.wikidata.org/wiki/Q3333679","display_name":"Probabilistic method","level":3,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5070/c65465679","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65465679","pdf_url":"https://escholarship.org/content/qt9862s2dg/qt9862s2dg.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},{"id":"pmh:doi:10.5070/C65465679","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S7407050878","display_name":"California Digital Library","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text/journal article"}],"best_oa_location":{"id":"doi:10.5070/c65465679","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65465679","pdf_url":"https://escholarship.org/content/qt9862s2dg/qt9862s2dg.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.44445037841796875,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311641","display_name":"University of Denver","ror":"https://ror.org/04w7skc03"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7127167246.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"parking":[1,41,55],"function":[2],"is":[3,16,65],"a":[4,117],"sequence":[5],"\\((\\pi_1,\\dots,":[6],"\\pi_n)\\)":[7],"of":[8,20,40,49,52,59,61,75,108],"positive":[9],"integers":[10],"such":[11],"that":[12],"if":[13],"\\(\\lambda_1\\leq\\cdots\\leq":[14],"\\lambda_n\\)":[15],"the":[17,38,46,68,85],"increasing":[18],"rearrangement":[19],"\\(\\pi_1,\\dots,\\pi_n\\),":[21],"then":[22],"\\(\\lambda_i\\leq":[23],"i\\)":[24],"for":[25],"\\(1\\leq":[26],"i\\leq":[27],"n\\).":[28],"In":[29],"this":[30],"paper":[31],"we":[32],"obtain":[33],"some":[34],"new":[35],"results":[36,99],"on":[37,54,84,92],"enumeration":[39],"functions.":[42,56],"We":[43],"will":[44],"consider":[45],"joint":[47,69],"distribution":[48,58],"several":[50],"sets":[51],"statistics":[53,64],"The":[57],"most":[60],"these":[62],"individual":[63],"known,":[66],"but":[67],"distributions":[70],"are":[71,78,111],"new.":[72],"Parking":[73,125],"functions":[74],"length":[76],"\\(n\\)":[77],"in":[79],"bijection":[80],"with":[81,94],"labelled":[82,105,127],"forests":[83],"vertex":[86],"set":[87],"\\([n]=\\{1,2,\\dots,n\\}\\)":[88],"(or":[89],"rooted":[90],"trees":[91],"\\([n]_0=\\{0,1,\\dots,n\\}\\)":[93],"root":[95],"\\(0\\)),":[96],"so":[97],"our":[98,109],"can":[100],"also":[101],"be":[102],"applied":[103],"to":[104,116],"forests.":[106],"Extensions":[107],"techniques":[110],"discussed,":[112],"including":[113],"an":[114],"extension":[115],"probabilistic":[118],"scenario.Mathematics":[119],"Subject":[120],"Classifications:":[121],"05A15,":[122],"60C05,":[123],"05A19Keywords:":[124],"function,":[126,130],"forest,":[128],"generating":[129],"recurrence,":[131],"Pollak's":[132],"circle":[133],"argument":[134]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2026-02-03T00:00:00"}