{"id":"https://openalex.org/W4415819062","doi":"https://doi.org/10.37236/13864","title":"Probabilistic (m, n)-Parking Functions","display_name":"Probabilistic (m, n)-Parking Functions","publication_year":2025,"publication_date":"2025-11-03","ids":{"openalex":"https://openalex.org/W4415819062","doi":"https://doi.org/10.37236/13864"},"language":null,"primary_location":{"id":"doi:10.37236/13864","is_oa":true,"landing_page_url":"https://doi.org/10.37236/13864","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i4p39/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i4p39/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049274003","display_name":"Pamela E. Harris","orcid":"https://orcid.org/0000-0002-3049-991X"},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pamela Harris","raw_affiliation_strings":["University of Wisconsin - Milwaukee"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin - Milwaukee","institution_ids":["https://openalex.org/I43579087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108003577","display_name":"Rodrigo Ribeiro","orcid":"https://orcid.org/0000-0002-0786-7569"},"institutions":[{"id":"https://openalex.org/I131651094","display_name":"University of Denver","ror":"https://ror.org/04w7skc03","country_code":"US","type":"education","lineage":["https://openalex.org/I131651094"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rodrigo Ribeiro","raw_affiliation_strings":["University of Denver"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Denver","institution_ids":["https://openalex.org/I131651094"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102204721","display_name":"Mei Yin","orcid":"https://orcid.org/0009-0006-3175-2469"},"institutions":[{"id":"https://openalex.org/I131651094","display_name":"University of Denver","ror":"https://ror.org/04w7skc03","country_code":"US","type":"education","lineage":["https://openalex.org/I131651094"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mei Yin","raw_affiliation_strings":["University of Denver"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Denver","institution_ids":["https://openalex.org/I131651094"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30376229,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12546","display_name":"Smart Parking Systems Research","score":0.8098000288009644,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12546","display_name":"Smart Parking Systems Research","score":0.8098000288009644,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.0357000008225441,"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/T10698","display_name":"Transportation Planning and Optimization","score":0.030400000512599945,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6018999814987183},{"id":"https://openalex.org/keywords/conditional-probability-distribution","display_name":"Conditional probability distribution","score":0.5934000015258789},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5455999970436096},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4964999854564667},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.49219998717308044},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.47040000557899475},{"id":"https://openalex.org/keywords/inverse-chi-squared-distribution","display_name":"Inverse-chi-squared distribution","score":0.4650999903678894},{"id":"https://openalex.org/keywords/conditional-probability","display_name":"Conditional probability","score":0.37549999356269836},{"id":"https://openalex.org/keywords/conditional-variance","display_name":"Conditional variance","score":0.36480000615119934}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.691100001335144},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6018999814987183},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.5934000015258789},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5455999970436096},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4964999854564667},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.49219998717308044},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47130000591278076},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.47040000557899475},{"id":"https://openalex.org/C57205106","wikidata":"https://www.wikidata.org/wiki/Q3258519","display_name":"Inverse-chi-squared distribution","level":4,"score":0.4650999903678894},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.37549999356269836},{"id":"https://openalex.org/C21430997","wikidata":"https://www.wikidata.org/wiki/Q5159279","display_name":"Conditional variance","level":4,"score":0.36480000615119934},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.3472000062465668},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C103982235","wikidata":"https://www.wikidata.org/wiki/Q7309594","display_name":"Regular conditional probability","level":4,"score":0.3409000039100647},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.33629998564720154},{"id":"https://openalex.org/C108882938","wikidata":"https://www.wikidata.org/wiki/Q274506","display_name":"Uniform distribution (continuous)","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3262999951839447},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3253999948501587},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2971000075340271},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.2969000041484833},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.2808000147342682},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.27889999747276306},{"id":"https://openalex.org/C72396439","wikidata":"https://www.wikidata.org/wiki/Q16000505","display_name":"Symmetric probability distribution","level":3,"score":0.27619999647140503},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C2776292839","wikidata":"https://www.wikidata.org/wiki/Q5179217","display_name":"Coverage probability","level":3,"score":0.2628999948501587},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.257999986410141},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/13864","is_oa":true,"landing_page_url":"https://doi.org/10.37236/13864","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i4p39/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/13864","is_oa":true,"landing_page_url":"https://doi.org/10.37236/13864","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i4p39/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311641","display_name":"University of Denver","ror":"https://ror.org/04w7skc03"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415819062.pdf","grobid_xml":"https://content.openalex.org/works/W4415819062.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,42,142],"establish":[4,158],"new":[5],"results":[6],"on":[7,73,100,119,149,178],"the":[8,44,48,55,74,80,89,95,101,105,109,116,131,145,164,169,175],"probabilistic":[9],"parking":[10,25,45],"model":[11],"(introduced":[12],"by":[13],"Durmi\u0107,":[14],"Han,":[15],"Harris,":[16],"Ribeiro,":[17],"and":[18,23,27,38,53,60,87,92,154,174],"Yin)":[19],"with":[20],"$m$":[21],"cars":[22],"$n$":[24,153],"spots":[26,129],"probability":[28,75],"parameter":[29,76],"$p":[30,39],"\\in":[31,40],"[0,1]$.":[32],"For":[33],"any":[34],"$m":[35],"\\leq":[36],"n$":[37],"[0,1]$,":[41],"study":[43,79],"preference":[46],"of":[47,58,97,112,127,172],"last":[49],"car,":[50],"denoted":[51],"$a_m$,":[52],"determine":[54],"conditional":[56,110,170],"distribution":[57,111,118,171,177],"$a_m$":[59,113,173],"compute":[61],"its":[62],"expected":[63],"value.":[64],"We":[65,78,157],"show":[66,93],"that":[67,94,159],"both":[68],"formulas":[69],"depict":[70],"explicit":[71],"dependence":[72],"$p$.":[77],"case":[81],"where":[82],"$m=cn$":[83],"for":[84,122],"some":[85],"$0<c<1$":[86],"investigate":[88],"asymptotic":[90],"behavior":[91],"presence":[96],"``extra":[98],"spots''":[99],"street":[102],"significantly":[103],"affects":[104],"rate":[106,133,147],"at":[107,181],"which":[108],"converges":[114],"to":[115,136],"uniform":[117,176],"$[n]$.":[120],"Even":[121],"small":[123],"$\\varepsilon=1-c$,":[124],"an":[125],"$\\varepsilon$-proportion":[126],"extra":[128],"reduces":[130],"convergence":[132,146],"from":[134],"$1/\\sqrt{n}$":[135],"$1/n$":[137],"when":[138],"$p\\neq":[139],"1/2$.":[140],"Additionally,":[141],"examine":[143],"how":[144],"depends":[148],"$c$,":[150],"while":[151],"keeping":[152],"$p$":[155],"fixed.":[156],"as":[160],"$c$":[161],"approaches":[162],"zero,":[163],"total":[165],"variation":[166],"distance":[167],"between":[168],"$[n]$":[179],"decreases":[180],"least":[182],"linearly":[183],"in":[184],"$c$.":[185]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-11-03T00:00:00"}