{"id":"https://openalex.org/W4412450049","doi":"https://doi.org/10.5070/c65265408","title":"Upho lattices I: examples and non-examples of cores","display_name":"Upho lattices I: examples and non-examples of cores","publication_year":2025,"publication_date":"2025-07-15","ids":{"openalex":"https://openalex.org/W4412450049","doi":"https://doi.org/10.5070/c65265408"},"language":"en","primary_location":{"id":"doi:10.5070/c65265408","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65265408","pdf_url":"https://escholarship.org/content/qt2w34138p/qt2w34138p.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt2w34138p/qt2w34138p.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5118996660","display_name":"Sam Hopkins","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sam Hopkins","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5118996660"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19342868,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.47360000014305115,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.47360000014305115,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3894129991531372}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3894129991531372}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5070/c65265408","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65265408","pdf_url":"https://escholarship.org/content/qt2w34138p/qt2w34138p.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},{"id":"pmh:doi:10.5070/C65265408","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S7407050878","display_name":"California Digital Library","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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/journal article"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt2w34138p","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/2w34138p","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"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":"Combinatorial Theory, vol 5, iss 2","raw_type":"article"}],"best_oa_location":{"id":"doi:10.5070/c65265408","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65265408","pdf_url":"https://escholarship.org/content/qt2w34138p/qt2w34138p.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412450049.pdf","grobid_xml":"https://content.openalex.org/works/W4412450049.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"A":[0],"poset":[1,15],"is":[2,16],"called":[3,46],"upper":[4],"homogeneous,":[5],"or":[6],"\"upho,\"":[7],"if":[8],"every":[9],"principal":[10],"order":[11],"filter":[12],"of":[13,64,95],"the":[14,19,74,96,104],"isomorphic":[17],"to":[18,40],"whole":[20],"poset.":[21],"We":[22,55],"study":[23],"(finite":[24],"type":[25],"\\(\\mathbb{N}\\)-graded)":[26],"upho":[27,36,65,97],"lattices,":[28,66,134,136,138],"with":[29],"an":[30],"eye":[31],"towards":[32],"their":[33],"classification.":[34],"Any":[35],"lattice":[37,45],"has":[38],"associated":[39],"it":[41],"a":[42],"finite":[43,58,82,115],"graded":[44,59],"its":[47,51],"core,":[48],"which":[49,57,100,112],"determines":[50],"rank":[52,128],"generating":[53,129],"function.":[54],"investigate":[56],"lattices":[60,83,98,116],"arise":[61,85],"as":[62,86],"cores":[63],"providing":[67],"both":[68],"positive":[69],"and":[70,88,92],"negative":[71],"results.":[72],"On":[73,103],"one":[75],"hand,":[76,106],"we":[77,89,107],"show":[78,108],"that":[79],"many":[80,114],"well-studied":[81],"do":[84],"cores,":[87],"present":[90],"combinatorial":[91],"algebraic":[93],"constructions":[94],"into":[99],"they":[101],"embed.":[102],"other":[105],"there":[109],"are":[110],"obstructions":[111],"prevent":[113],"from":[117],"being":[118],"cores.Mathematics":[119],"Subject":[120],"Classifications:":[121],"06A07,":[122],"05B35,":[123],"06C10,":[124],"20M32Keywords:":[125],"Upho":[126],"posets,":[127],"functions,":[130],"characteristic":[131],"polynomials,":[132],"geometric":[133],"supersolvable":[135],"Dowling":[137],"Garside":[139],"monoids":[140]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}