{"id":"https://openalex.org/W7207878258","doi":"https://doi.org/10.48550/arxiv.2609.02491","title":"Generalised Random Parking for Trapeziums on a Strip","display_name":"Generalised Random Parking for Trapeziums on a Strip","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7207878258","doi":"https://doi.org/10.48550/arxiv.2609.02491"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.02491","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02491","pdf_url":"https://arxiv.org/pdf/2609.02491","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.02491","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027687184","display_name":"David Kramer-Bang","orcid":"https://orcid.org/0000-0003-0384-4172","observed_orcids":["https://orcid.org/0000-0003-0384-4172"]},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Kramer-Bang, David","raw_affiliation_strings":["Aarhus University , Department of Mathematics , DK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aarhus University , Department of Mathematics , DK","institution_ids":["https://openalex.org/I204337017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022333380","display_name":"Stjepan \u0160ebek","orcid":"https://orcid.org/0000-0002-1802-1542","observed_orcids":["https://orcid.org/0000-0002-1802-1542"]},"institutions":[{"id":"https://openalex.org/I181343428","display_name":"University of Zagreb","ror":"https://ror.org/00mv6sv71","country_code":"HR","type":"education","lineage":["https://openalex.org/I181343428"]},{"id":"https://openalex.org/I4390039327","display_name":"Faculty of Electrical Engineering and Computing in Zagreb","ror":"https://ror.org/04e90ca47","country_code":"HR","type":"education","lineage":["https://openalex.org/I181343428","https://openalex.org/I4390039327"]}],"countries":["HR"],"is_corresponding":false,"raw_author_name":"\u0160ebek, Stjepan","raw_affiliation_strings":["University of Zagreb Faculty of Electrical Engineering and Computing ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Zagreb Faculty of Electrical Engineering and Computing ,","institution_ids":["https://openalex.org/I181343428","https://openalex.org/I4390039327"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.8568999767303467,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.8568999767303467,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.04569999873638153,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.033799998462200165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/strip-packing","display_name":"strip packing","score":0.4650000035762787}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7646999955177307},{"id":"https://openalex.org/C98653994","wikidata":"https://www.wikidata.org/wiki/Q875937","display_name":"Isosceles triangle","level":2,"score":0.7554000020027161},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.7504000067710876},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5633000135421753},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4991999864578247},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.43939998745918274},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.41999998688697815},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40849998593330383},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.3637999892234802},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35850000381469727},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.30329999327659607},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28679999709129333},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.27619999647140503}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.02491","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02491","pdf_url":"https://arxiv.org/pdf/2609.02491","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.02491","doi":"https://doi.org/10.48550/arxiv.2609.02491","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.02491","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.02491","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02491","pdf_url":"https://arxiv.org/pdf/2609.02491","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1210808807","display_name":"Isaac Newton Institute for Mathematical Sciences (INI)","funder_award_id":"EP/Z000580/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G160912597","display_name":"Geometric properties and potential theory of stochastic processes","funder_award_id":"IP-2022-10-2277","funder_id":"https://openalex.org/F4320322674","funder_display_name":"Hrvatska Zaklada za Znanost"},{"id":"https://openalex.org/G3408410167","display_name":null,"funder_award_id":"IP-2022-10","funder_id":"https://openalex.org/F4320322674","funder_display_name":"Hrvatska Zaklada za Znanost"},{"id":"https://openalex.org/G3611179903","display_name":null,"funder_award_id":"2021-2026","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4938354709","display_name":null,"funder_award_id":"2021-2026","funder_id":"https://openalex.org/F4320322674","funder_display_name":"Hrvatska Zaklada za Znanost"}],"funders":[{"id":"https://openalex.org/F4320310928","display_name":"Sveu\u010dili\u0161te u Zagrebu","ror":"https://ror.org/00mv6sv71"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322674","display_name":"Hrvatska Zaklada za Znanost","ror":"https://ror.org/03n51vw80"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207878258.pdf","grobid_xml":"https://content.openalex.org/works/W7207878258.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1968876433","https://openalex.org/W1974288493","https://openalex.org/W2008546827","https://openalex.org/W2024362988","https://openalex.org/W2090590500","https://openalex.org/W2322943362","https://openalex.org/W2327393874","https://openalex.org/W2481468714","https://openalex.org/W3108923753","https://openalex.org/W4230392815"],"related_works":["https://openalex.org/W4408972560","https://openalex.org/W2567079279","https://openalex.org/W3122737070","https://openalex.org/W2507563413","https://openalex.org/W6929273431","https://openalex.org/W2997984195","https://openalex.org/W7112330157","https://openalex.org/W4285355245","https://openalex.org/W2087394128","https://openalex.org/W2067264186"],"abstract_inverted_index":{"In":[0,79],"this":[1],"article,":[2],"we":[3,99],"study":[4],"a":[5,19,117,127,132],"generalisation":[6],"of":[7,32,35,63,75,110],"R\u00e9nyi's":[8],"car-parking":[9],"problem":[10],"in":[11,30],"which":[12],"isosceles":[13],"trapeziums":[14],"are":[15],"sequentially":[16],"deposited":[17,64,77],"on":[18,72,107],"strip.":[20],"We":[21,49],"derive":[22],"an":[23],"explicit":[24],"formula":[25],"for":[26,55],"the":[27,33,36,40,57,61,73,76,82,93,102,108,111,122],"parking":[28,103],"constant":[29,104],"terms":[31],"lengths":[34,114],"two":[37,86,112],"bases,":[38],"recovering":[39],"classical":[41],"rectangular":[42],"and":[43,60,115],"triangular":[44],"models":[45],"as":[46],"special":[47],"cases.":[48],"further":[50],"obtain":[51],"quantitative":[52],"finite-size":[53],"asymptotics":[54],"both":[56],"expected":[58],"number":[59],"variance":[62],"trapeziums,":[65],"with":[66],"convergence":[67],"rates":[68],"that":[69,101,121],"depend":[70],"explicitly":[71],"geometry":[74],"particle.":[78],"particular,":[80],"although":[81],"recursive":[83],"construction":[84],"involves":[85],"different":[87],"substrate":[88],"geometries,":[89],"their":[90],"variances":[91],"have":[92],"same":[94],"leading":[95],"asymptotic":[96],"density.":[97],"Finally,":[98],"show":[100],"depends":[105],"non-monotonically":[106],"ratio":[109],"base":[113],"possesses":[116],"unique":[118],"minimiser,":[119],"so":[120],"least":[123],"efficient":[124],"shape":[125],"is":[126],"genuine":[128],"trapezium":[129],"rather":[130],"than":[131],"triangle.":[133]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-04T00:00:00"}