{"id":"https://openalex.org/W4283330426","doi":"https://doi.org/10.37236/11373","title":"Rank-Metric Lattices","display_name":"Rank-Metric Lattices","publication_year":2023,"publication_date":"2023-01-13","ids":{"openalex":"https://openalex.org/W4283330426","doi":"https://doi.org/10.37236/11373"},"language":"en","primary_location":{"id":"doi:10.37236/11373","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11373","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i1p4/pdf","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":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i1p4/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026871112","display_name":"Giuseppe Cotardo","orcid":"https://orcid.org/0000-0001-9178-3941"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":true,"raw_author_name":"Giuseppe Cotardo","raw_affiliation_strings":["University College Dublin"],"affiliations":[{"raw_affiliation_string":"University College Dublin","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025356502","display_name":"Alberto Ravagnani","orcid":"https://orcid.org/0000-0001-5901-9484"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Alberto Ravagnani","raw_affiliation_strings":["Eindhoven University of Technology"],"affiliations":[{"raw_affiliation_string":"Eindhoven University of Technology","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026871112"],"corresponding_institution_ids":["https://openalex.org/I100930933"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00234311,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.6172000169754028,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11130","display_name":"Coding theory and cryptography","score":0.6172000169754028,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.24549999833106995,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.03500000014901161,"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/rank","display_name":"Rank (graph theory)","score":0.7595698833465576},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7125802040100098},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.7081550359725952},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6167334318161011},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.507037878036499},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4042910635471344},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06063804030418396}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7595698833465576},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7125802040100098},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7081550359725952},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6167334318161011},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.507037878036499},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4042910635471344},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06063804030418396},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.37236/11373","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11373","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i1p4/pdf","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:2206.09284","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2206.09284","pdf_url":"https://arxiv.org/pdf/2206.09284","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":"pmh:oai:vtechworks.lib.vt.edu:10919/114221","is_oa":true,"landing_page_url":"http://hdl.handle.net/10919/114221","pdf_url":"https://vtechworks.lib.vt.edu/bitstreams/c6b8a8ee-fa24-4e89-8a39-37d9779d0e60/download","source":{"id":"https://openalex.org/S4306400248","display_name":"VTechWorks (Virginia Tech)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I859038795","host_organization_name":"Virginia Tech","host_organization_lineage":["https://openalex.org/I859038795"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:pure.tue.nl:openaire/db38c5e8-f257-466c-9ea3-8aaf7b6714e8","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/db38c5e8-f257-466c-9ea3-8aaf7b6714e8","pdf_url":"https://pure.tue.nl/ws/files/292958414/11373_PDF_file_43355_1_10_20230104.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"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":"Cotardo, G & Ravagnani, A 2023, 'Rank-Metric Lattices', The Electronic Journal of Combinatorics, vol. 30, no. 1, P1.4. https://doi.org/10.37236/11373","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.tue.nl:publications/db38c5e8-f257-466c-9ea3-8aaf7b6714e8","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85146183294&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"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":"Cotardo, G & Ravagnani, A 2023, 'Rank-Metric Lattices', The Electronic Journal of Combinatorics, vol. 30, no. 1, P1.4. https://doi.org/10.37236/11373","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:tue:oai:pure.tue.nl:publications/db38c5e8-f257-466c-9ea3-8aaf7b6714e8","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/db38c5e8-f257-466c-9ea3-8aaf7b6714e8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Journal of Combinatorics, 30(1):P1.4. Electronic Journal of Combinatorics","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2206.09284","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2206.09284","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/11373","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11373","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i1p4/pdf","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":[{"id":"https://openalex.org/G1681793210","display_name":null,"funder_award_id":"KLEIN","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G5618363122","display_name":null,"funder_award_id":"VI.Vidi.203.045","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6009445997","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G660757063","display_name":null,"funder_award_id":"OCENW.KLEIN.539","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4283330426.pdf"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1525281720","https://openalex.org/W1538550540","https://openalex.org/W1785358459","https://openalex.org/W1898022286","https://openalex.org/W1961596217","https://openalex.org/W1967951304","https://openalex.org/W2041659729","https://openalex.org/W2057503509","https://openalex.org/W2062070396","https://openalex.org/W2063121374","https://openalex.org/W2086297027","https://openalex.org/W2095547380","https://openalex.org/W2197225813","https://openalex.org/W2523329746","https://openalex.org/W2576087124","https://openalex.org/W2580044016","https://openalex.org/W2618233521","https://openalex.org/W2795369542","https://openalex.org/W2799518918","https://openalex.org/W2974757590","https://openalex.org/W2994132020","https://openalex.org/W3096146904","https://openalex.org/W3103202762","https://openalex.org/W6761170890","https://openalex.org/W6820137623"],"related_works":["https://openalex.org/W35471102","https://openalex.org/W28145769","https://openalex.org/W1237404","https://openalex.org/W22502614","https://openalex.org/W12472064","https://openalex.org/W53942402","https://openalex.org/W42816290","https://openalex.org/W37374799","https://openalex.org/W38290255","https://openalex.org/W52854976"],"abstract_inverted_index":{"We":[0,34,46],"introduce":[1,106],"the":[2,10,22,37,74,85,98,107],"class":[3],"of":[4,12,24,73,87,100,109,112],"rank-metric":[5,39,51,89,101,114],"geometric":[6],"lattices":[7,17,40,52],"and":[8,41,59,83,116,123],"initiate":[9],"study":[11],"their":[13,43,70,118],"structural":[14],"properties.":[15],"Rank-metric":[16],"can":[18],"be":[19],"seen":[20],"as":[21,120,124],"$q$-analogues":[23],"higher-weight":[25],"Dowling":[26,30],"lattices,":[27],"defined":[28],"by":[29],"himself":[31],"in":[32,94],"1971.":[33],"fully":[35],"characterize":[36],"supersolvable":[38],"compute":[42],"characteristic":[44,54],"polynomials.":[45],"then":[47],"concentrate":[48],"on":[49,69,80,84],"small":[50],"whose":[53],"polynomial":[55],"we":[56,92,105],"cannot":[57],"compute,":[58],"provide":[60],"a":[61,66,113],"formula":[62],"for":[63,127],"them":[64],"under":[65],"polynomiality":[67],"assumption":[68],"Whitney":[71],"numbers":[72],"first":[75],"kind.":[76],"The":[77],"proof":[78],"relies":[79],"computational":[81],"results":[82],"theory":[86],"vector":[88],"codes,":[90],"which":[91],"review":[93],"this":[95],"paper":[96],"from":[97],"perspective":[99],"lattices.":[102],"More":[103],"precisely,":[104],"notion":[108],"lattice-rank":[110],"weights":[111],"code":[115,125],"investigate":[117],"properties":[119],"combinatorial":[121],"invariants":[122],"distinguishers":[126],"inequivalent":[128],"codes.":[129]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2022-06-24T00:00:00"}