{"id":"https://openalex.org/W4415310501","doi":"https://doi.org/10.1007/s11083-025-09710-3","title":"Order Dimension, Grids, and Products","display_name":"Order Dimension, Grids, and Products","publication_year":2025,"publication_date":"2025-10-18","ids":{"openalex":"https://openalex.org/W4415310501","doi":"https://doi.org/10.1007/s11083-025-09710-3"},"language":"en","primary_location":{"id":"doi:10.1007/s11083-025-09710-3","doi":"https://doi.org/10.1007/s11083-025-09710-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-025-09710-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-025-09710-3.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11083-025-09710-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005468020","display_name":"Stefan Felsner","orcid":"https://orcid.org/0000-0002-6150-1998","observed_orcids":["https://orcid.org/0000-0002-6150-1998"]},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Stefan Felsner","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028248747","display_name":"Torsten M\u00fctze","orcid":"https://orcid.org/0000-0002-6383-7436","observed_orcids":["https://orcid.org/0000-0002-6383-7436"]},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Torsten M\u00fctze","raw_affiliation_strings":["Universit\u00e4t Kassel, Kassel, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Kassel, Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]}]},{"author_position":"last","author":{"id":null,"display_name":"Maximilian Wittmann","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Maximilian Wittmann","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005468020"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":2.5899,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.89317232,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":96},"biblio":{"volume":"42","issue":"3","first_page":"811","last_page":"827"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9901999831199646,"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":0.9901999831199646,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.00279999990016222,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.002099999925121665,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/order-dimension","display_name":"order dimension","score":0.9819999933242798},{"id":"https://openalex.org/keywords/fences","display_name":"fences","score":0.5830000042915344},{"id":"https://openalex.org/keywords/crown","display_name":"crowns","score":0.8769999742507935},{"id":"https://openalex.org/keywords/covering-properties","display_name":"covering properties","score":0.8140000104904175},{"id":"https://openalex.org/keywords/reuters","display_name":"Reuters","score":0.5649999976158142}],"concepts":[{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.859000027179718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8361999988555908},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.829800009727478},{"id":"https://openalex.org/C2779652578","wikidata":"https://www.wikidata.org/wiki/Q5442977","display_name":"Fence (mathematics)","level":2,"score":0.6990000009536743},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6162999868392944},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6083999872207642},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.5741999745368958},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48399999737739563},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41690000891685486},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4072999954223633},{"id":"https://openalex.org/C2985459651","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Ordered set","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3944000005722046},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.3928000032901764},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.34369999170303345},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.2806999981403351}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11083-025-09710-3","doi":"https://doi.org/10.1007/s11083-025-09710-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-025-09710-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-025-09710-3.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},{"id":"pmh:oai:depositonce.tu-berlin.de:11303/26097","doi":null,"is_oa":true,"landing_page_url":"https://depositonce.tu-berlin.de/handle/11303/26097","pdf_url":null,"source":{"id":"https://openalex.org/S4406922277","display_name":"DepositOnce","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.14279/depositonce-24925","doi":"https://doi.org/10.14279/depositonce-24925","is_oa":true,"landing_page_url":"https://doi.org/10.14279/depositonce-24925","pdf_url":null,"source":{"id":"https://openalex.org/S7407052985","display_name":"Technische Universit\u00e4t Berlin \u2013 Universit\u00e4tsbibliothek","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4577782","host_organization_name":"Technische Universit\u00e4t Berlin","host_organization_lineage":["https://openalex.org/I4577782"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"doi:10.1007/s11083-025-09710-3","doi":"https://doi.org/10.1007/s11083-025-09710-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-025-09710-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-025-09710-3.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4901133172","display_name":"Principles of combinatorial generation","funder_award_id":"GA22-15272S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G992026124","display_name":"Grundlagen kombinatorischer Algorithmen","funder_award_id":"522790373","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415310501.pdf","grobid_xml":"https://content.openalex.org/works/W4415310501.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1513322989","https://openalex.org/W1574212655","https://openalex.org/W2000041159","https://openalex.org/W2033344392","https://openalex.org/W2047238477","https://openalex.org/W2053876549","https://openalex.org/W2068654529","https://openalex.org/W2078340224","https://openalex.org/W2083176195","https://openalex.org/W2085823872","https://openalex.org/W2247321008","https://openalex.org/W2318940310","https://openalex.org/W2325654786","https://openalex.org/W4319782100","https://openalex.org/W6911935754"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Interested":[1],"in":[2,105,147,181],"the":[3,6,17,120,125,135,150,184,190],"dimension":[4,106,121],"of":[5,9,19,28,122,183,187,189],"face":[7],"lattices":[8],"d":[10],"-dimensional":[11],"grids,":[12],"we":[13,117],"are":[14,127],"led":[15],"to":[16],"study":[18],"fences":[20],"and":[21,37,99,129,144,163],"their":[22],"products.":[23],"This":[24],"yields":[25],"a":[26,33,102,115],"characterization":[27],"generalized":[29,34],"fences:":[30],"F":[31,51],"is":[32,101,114],"fence":[35,116],"if":[36,39],"only":[38],"$$\\dim":[40,66,153,164],"(P\\times":[41],"F)":[42],"\\leqslant":[43],"\\dim":[44,71,74,167],"(P)":[45,72,165],"+1$$":[46],"dim":[47,54,77,84,89,157,169,174],"(":[48,55,78,85,90,158,170,175],"P":[49,56,63,79,86,98,159,171],"\u00d7":[50,80,160],")":[52,57,82,87,92,162,172,177],"\u2a7d":[53],"+":[58,73,88,166,173],"1":[59],"for":[60,95,141],"every":[61],"poset":[62],".":[64],"Whether":[65],"(P":[67,154],"\\times":[68,155],"Q)":[69],"\\geqslant":[70],"(Q)":[75],"-2$$":[76],"Q":[81,91,100,161,176],"\u2a7e":[83],"-":[93],"2":[94],"all":[96],"posets":[97],"long-standing":[103],"question":[104],"theory.":[107],"Having":[108],"understood":[109],"products":[110,123],"where":[111,124],"one":[112,188],"factor":[113],"further":[118],"investigate":[119],"factors":[126],"crowns":[128],"other":[130],"3-dimensional":[131],"posets.":[132],"We":[133],"reconsider":[134],"covering":[136,185],"property":[137],"defined":[138],"by":[139],"Reuter":[140],"Ferrers":[142],"relations":[143],"show":[145],"that":[146],"many":[148],"cases":[149],"gap":[151],"between":[152],"Q)$$":[156],"(Q)$$":[168],"can":[178],"be":[179],"explained":[180],"terms":[182],"properties":[186],"factors.":[191]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-18T00:00:00"}