{"id":"https://openalex.org/W2271367836","doi":"https://doi.org/10.37236/5940","title":"A Decomposition of Parking Functions by Undesired Spaces","display_name":"A Decomposition of Parking Functions by Undesired Spaces","publication_year":2016,"publication_date":"2016-08-19","ids":{"openalex":"https://openalex.org/W2271367836","doi":"https://doi.org/10.37236/5940","mag":"2271367836"},"language":"en","primary_location":{"id":"doi:10.37236/5940","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5940","pdf_url":null,"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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/5940","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090185426","display_name":"Melody Bruce","orcid":null},"institutions":[{"id":"https://openalex.org/I103406327","display_name":"Western Carolina University","ror":"https://ror.org/010h78f45","country_code":"US","type":"education","lineage":["https://openalex.org/I103406327"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Melody Bruce","raw_affiliation_strings":["Western Carolina University"],"affiliations":[{"raw_affiliation_string":"Western Carolina University","institution_ids":["https://openalex.org/I103406327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064110623","display_name":"Michael Dougherty","orcid":"https://orcid.org/0000-0002-5231-2730"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Dougherty","raw_affiliation_strings":["University of California, Santa Barbara","University of California Santa Barbara"],"affiliations":[{"raw_affiliation_string":"University of California, Santa Barbara","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"University of California Santa Barbara","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031285405","display_name":"Max Hlavacek","orcid":"https://orcid.org/0000-0002-5229-1909"},"institutions":[{"id":"https://openalex.org/I133543626","display_name":"Harvey Mudd College","ror":"https://ror.org/025ecfn45","country_code":"US","type":"education","lineage":["https://openalex.org/I133543626"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Max Hlavacek","raw_affiliation_strings":["Harvey Mudd College","Harvey Mudd Coll"],"affiliations":[{"raw_affiliation_string":"Harvey Mudd College","institution_ids":["https://openalex.org/I133543626"]},{"raw_affiliation_string":"Harvey Mudd Coll","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036546446","display_name":"Ryo Kudo","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ryo Kudo","raw_affiliation_strings":["University of California, Los Angeles","University of California-Los Angeles"],"affiliations":[{"raw_affiliation_string":"University of California, Los Angeles","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"University of California-Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028932047","display_name":"Ian Nicolas","orcid":null},"institutions":[{"id":"https://openalex.org/I4210149261","display_name":"Pacific University","ror":"https://ror.org/059z5w858","country_code":"US","type":"education","lineage":["https://openalex.org/I4210149261"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ian Nicolas","raw_affiliation_strings":["Pacific University"],"affiliations":[{"raw_affiliation_string":"Pacific University","institution_ids":["https://openalex.org/I4210149261"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5090185426"],"corresponding_institution_ids":["https://openalex.org/I103406327"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.04260758,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"23","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":1.0,"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":1.0,"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/T11716","display_name":"Random Matrices and Applications","score":0.9961000084877014,"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"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9911999702453613,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.7741756439208984},{"id":"https://openalex.org/keywords/hasse-diagram","display_name":"Hasse diagram","score":0.7516387104988098},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.7105376720428467},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6836668252944946},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5969284176826477},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5935324430465698},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5425764322280884},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.490861713886261},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.4436514973640442},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4180018901824951},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0806104838848114}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7741756439208984},{"id":"https://openalex.org/C140002607","wikidata":"https://www.wikidata.org/wiki/Q901446","display_name":"Hasse diagram","level":3,"score":0.7516387104988098},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.7105376720428467},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6836668252944946},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5969284176826477},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5935324430465698},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5425764322280884},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.490861713886261},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4436514973640442},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4180018901824951},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0806104838848114},{"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/5940","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5940","pdf_url":null,"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"},{"id":"pmh:oai:arXiv.org:1602.02175","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.02175","pdf_url":"https://arxiv.org/pdf/1602.02175","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2271367836","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1602.02175","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1602.02175","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1602.02175","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/5940","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5940","pdf_url":null,"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":[{"score":0.5199999809265137,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1526839219","https://openalex.org/W1579213680","https://openalex.org/W1972912363","https://openalex.org/W1990854005","https://openalex.org/W2020518828","https://openalex.org/W2032690805"],"related_works":["https://openalex.org/W2963727630","https://openalex.org/W2767240619","https://openalex.org/W2577246944","https://openalex.org/W2120099164","https://openalex.org/W2158235205","https://openalex.org/W3112306649","https://openalex.org/W2044557803","https://openalex.org/W2949646581","https://openalex.org/W2075375246","https://openalex.org/W2089049012","https://openalex.org/W66956527","https://openalex.org/W2952213428","https://openalex.org/W2743384536","https://openalex.org/W2952899878","https://openalex.org/W1898667234","https://openalex.org/W2939142289","https://openalex.org/W2937891156","https://openalex.org/W1963809736","https://openalex.org/W2006159741","https://openalex.org/W2964291872"],"abstract_inverted_index":{"There":[0],"is":[1,37],"a":[2,9,32,47,80,85,91],"well-known":[3],"bijection":[4],"between":[5],"parking":[6,30,50],"functions":[7,31,51],"of":[8,15,29,40,49,83],"fixed":[10],"length":[11],"and":[12,58,90,105],"maximal":[13,43],"chains":[14],"the":[16,38,41,54,63,72],"noncrossing":[17,73],"partition":[18,74],"lattice":[19,75],"which":[20],"we":[21],"can":[22],"use":[23],"to":[24,26],"associate":[25],"each":[27],"set":[28],"poset":[33],"whose":[34],"Hasse":[35],"diagram":[36],"union":[39],"corresponding":[42,64],"chains.":[44],"We":[45,95],"introduce":[46],"decomposition":[48],"based":[52],"on":[53],"largest":[55],"number":[56],"omitted":[57],"prove":[59],"several":[60],"theorems":[61],"about":[62],"posets.":[65],"In":[66],"particular,":[67],"they":[68],"share":[69],"properties":[70],"with":[71,99],"such":[76],"as":[77],"local":[78],"self-duality,":[79],"nice":[81],"characterization":[82],"intervals,":[84],"readily":[86],"computable":[87],"M\u00f6bius":[88],"function,":[89],"symmetric":[92],"chain":[93],"decomposition.":[94],"also":[96],"explore":[97],"connections":[98],"order":[100],"complexes,":[101],"labeled":[102],"Dyck":[103],"paths,":[104],"rooted":[106],"forests.":[107]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
