{"id":"https://openalex.org/W2725661400","doi":"https://doi.org/10.37236/7124","title":"Symmetric Chain Decompositions of Products of Posets with Long Chains","display_name":"Symmetric Chain Decompositions of Products of Posets with Long Chains","publication_year":2018,"publication_date":"2018-03-29","ids":{"openalex":"https://openalex.org/W2725661400","doi":"https://doi.org/10.37236/7124","mag":"2725661400"},"language":"en","primary_location":{"id":"doi:10.37236/7124","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7124","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/10.37236/7124","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103367375","display_name":"Stefan David","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Stefan David","raw_affiliation_strings":["Trinity College, Cambridge University"],"affiliations":[{"raw_affiliation_string":"Trinity College, Cambridge University","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046252542","display_name":"Hunter Spink","orcid":null},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hunter Spink","raw_affiliation_strings":["Harvard University","Harvard University ,"],"affiliations":[{"raw_affiliation_string":"Harvard University","institution_ids":["https://openalex.org/I2801851002"]},{"raw_affiliation_string":"Harvard University ,","institution_ids":["https://openalex.org/I2801851002"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086003488","display_name":"Marius Tiba","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Marius Tiba","raw_affiliation_strings":["Trinity Hall, Cambridge University","Trinity Hall Cambridge University"],"affiliations":[{"raw_affiliation_string":"Trinity Hall, Cambridge University","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Trinity Hall Cambridge University","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103367375"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":0.80895886,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65933648,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"25","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9986000061035156,"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":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.7691612243652344},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.7509326934814453},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6971607208251953},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.6300227046012878},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6070864200592041},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5643146634101868},{"id":"https://openalex.org/keywords/surjective-function","display_name":"Surjective function","score":0.5230075716972351},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5156247019767761},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19338542222976685},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06671193242073059},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05468568205833435}],"concepts":[{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.7691612243652344},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7509326934814453},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6971607208251953},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.6300227046012878},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6070864200592041},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5643146634101868},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.5230075716972351},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5156247019767761},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19338542222976685},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06671193242073059},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05468568205833435}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/7124","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7124","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:1706.08546","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1706.08546","pdf_url":"https://arxiv.org/pdf/1706.08546","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":"doi:10.48550/arxiv.1706.08546","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1706.08546","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"},{"id":"mag:2725661400","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.37236/7124","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7124","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1974280274","https://openalex.org/W2062952844","https://openalex.org/W2604650262"],"related_works":["https://openalex.org/W1673295963","https://openalex.org/W1500354427","https://openalex.org/W3139590225","https://openalex.org/W422457422","https://openalex.org/W2972543214","https://openalex.org/W2042325565","https://openalex.org/W2729580200","https://openalex.org/W2345320385","https://openalex.org/W2171443875","https://openalex.org/W2886866895","https://openalex.org/W2004327230","https://openalex.org/W2952877554","https://openalex.org/W2062024946","https://openalex.org/W2033944624","https://openalex.org/W2098979446","https://openalex.org/W1972747917","https://openalex.org/W2952970770","https://openalex.org/W2314371715","https://openalex.org/W2091339148","https://openalex.org/W2972422066"],"abstract_inverted_index":{"We":[0],"ask":[1],"if":[2],"there":[3,117],"exists":[4,118],"a":[5,25,99,112,119,150,160],"symmetric":[6,58,92,123,168,178],"chain":[7,18,23,59,64,93,124,169,179],"decomposition":[8],"of":[9,27,57,69,82,101,126,144,171,181],"the":[10,28,67,70,78,86,142],"cuboid":[11],"$Q_k":[12],"\\times":[13,128,132,173,183],"n$":[14,133],"such":[15],"that":[16,110,140],"no":[17,22],"is":[19,40],"taut,":[20],"i.e.":[21],"has":[24,149],"subchain":[26],"form":[29],"$(a_1,\\ldots,":[30],"a_k,0)\\prec":[31],"\\cdots\\prec":[32],"(a_1,\\ldots,a_k,n-1)$.":[33],"In":[34,106],"this":[35,39,74],"paper,":[36],"we":[37,108,157],"show":[38,109],"true":[41],"precisely":[42],"when":[43,54],"$k":[44],"\\ge":[45],"5$":[46],"and":[47,103,130,153],"$n\\ge":[48],"3$.":[49],"This":[50],"question":[51],"arises":[52],"naturally":[53],"considering":[55],"products":[56],"decompositions":[60,65,71,94,125,170,180,187,192],"which":[61,185],"induce":[62],"orthogonal":[63,91],"\u2014":[66],"existence":[68,143],"provided":[72],"in":[73],"paper":[75],"unexpectedly":[76],"resolves":[77],"most":[79],"difficult":[80],"case":[81],"previous":[83],"work":[84],"by":[85],"second":[87],"author":[88],"on":[89,98],"almost":[90],"(2017),":[95],"making":[96],"progress":[97],"conjecture":[100],"Shearer":[102],"Kleitman":[104],"(1979).":[105],"general,":[107],"for":[111,134],"finite":[113],"graded":[114],"poset":[115],"$P$,":[116],"canonical":[120,161],"bijection":[121],"between":[122],"$P":[127,131,172,182],"m$":[129],"$m,":[135],"n\\ge":[136],"rk(P)":[137],"+":[138,175],"1$,":[139],"preserves":[141],"taut":[145,189,194],"chains.":[146,195],"If":[147],"$P$":[148],"unique":[151],"maximal":[152],"minimal":[154],"element,":[155],"then":[156],"also":[158],"produce":[159],"$(rk(P)":[162],"+1)$":[163],"to":[164,177,191],"$1$":[165],"surjection":[166],"from":[167],"(rk(P)":[174],"1)$":[176],"rk(P)$":[184],"sends":[186],"with":[188,193],"chains":[190]},"counts_by_year":[{"year":2019,"cited_by_count":2}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}