{"id":"https://openalex.org/W4319442161","doi":"https://doi.org/10.3934/amc.2023001","title":"On covering problems in hierarchical poset spaces","display_name":"On covering problems in hierarchical poset spaces","publication_year":2023,"publication_date":"2023-02-07","ids":{"openalex":"https://openalex.org/W4319442161","doi":"https://doi.org/10.3934/amc.2023001"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2023001","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2023001","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=63c68b2cb5351f4889afec4a","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/data/article/export-pdf?id=63c68b2cb5351f4889afec4a","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022464699","display_name":"Marcos Vin\u00edcius Pereira Spreafico","orcid":"https://orcid.org/0000-0003-0423-9310"},"institutions":[{"id":"https://openalex.org/I122558511","display_name":"Universidade Federal de Mato Grosso do Sul","ror":"https://ror.org/0366d2847","country_code":"BR","type":"education","lineage":["https://openalex.org/I122558511"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Marcos Vinicius Pereira Spreafico","raw_affiliation_strings":["Institute of Mathematics, Federal University of Mato Grosso do Sul, Campo Grande -MS -Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Federal University of Mato Grosso do Sul, Campo Grande -MS -Brazil","institution_ids":["https://openalex.org/I122558511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081674560","display_name":"Ot\u00e1vio Jos\u00e9 Neto Tinoco Neves dos Santos","orcid":null},"institutions":[{"id":"https://openalex.org/I2802295813","display_name":"Universidade Estadual de Mato Grosso do Sul","ror":"https://ror.org/02ggt9460","country_code":"BR","type":"education","lineage":["https://openalex.org/I2802295813"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Ot\u00e1vio Jos\u00e9 Neto Tinoco Neves dos Santos","raw_affiliation_strings":["State University of Mato Grosso do Sul, Dourados - MS - Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State University of Mato Grosso do Sul, Dourados - MS - Brazil","institution_ids":["https://openalex.org/I2802295813"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083404824","display_name":"Roberto Assis Machado","orcid":"https://orcid.org/0000-0003-0282-0742"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Roberto Assis Machado","raw_affiliation_strings":["School of Mathematical and Statistical Sciences, Clemson University, Clemson - South Carolina - U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences, Clemson University, Clemson - South Carolina - U.S.A","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081674560"],"corresponding_institution_ids":["https://openalex.org/I2802295813"],"apc_list":null,"apc_paid":null,"fwci":0.1427,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.42602668,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"5","first_page":"1471","last_page":"1479"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9954000115394592,"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":0.9954000115394592,"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/T11567","display_name":"semigroups and automata theory","score":0.9951000213623047,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9937999844551086,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9296993017196655},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.8788139224052429},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4833102226257324},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4602033793926239}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9296993017196655},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.8788139224052429},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4833102226257324},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4602033793926239}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2023001","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2023001","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=63c68b2cb5351f4889afec4a","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2023001","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2023001","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=63c68b2cb5351f4889afec4a","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320323354","display_name":"Funda\u00e7\u00e3o de Apoio ao Desenvolvimento do Ensino, Ci\u00eancia e Tecnologia do Estado de Mato Grosso do Sul","ror":"https://ror.org/05jtrt935"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4319442161.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1936001028","https://openalex.org/W2000719185","https://openalex.org/W2007472708","https://openalex.org/W2015900067","https://openalex.org/W2031242533","https://openalex.org/W2043474783","https://openalex.org/W2057014687","https://openalex.org/W2073599112","https://openalex.org/W2077595184","https://openalex.org/W2078022344","https://openalex.org/W2135232882","https://openalex.org/W2136319083","https://openalex.org/W2157562358","https://openalex.org/W2408047831","https://openalex.org/W2899114616","https://openalex.org/W2921369366","https://openalex.org/W2951522541","https://openalex.org/W2962953446"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2106070061","https://openalex.org/W4390961156","https://openalex.org/W4394660572","https://openalex.org/W1489559156","https://openalex.org/W4312224320","https://openalex.org/W1963087247","https://openalex.org/W2347443236","https://openalex.org/W4205203210","https://openalex.org/W1979597421"],"abstract_inverted_index":{"Given":[0],"a":[1,8,133],"ground":[2],"set":[3],"$":[4,6,10,12,16,32,34,40,80,84,123,137],"\\mathcal{U}":[5,17,41],"and":[7,58,68,83],"collection":[9],"\\mathcal{C}":[11],"of":[13,15,28,79,136],"subsets":[14],"$,":[18],"we":[19,120],"investigate":[20],"the":[21,26,29,38,53,55,62,66,69,72,92,104,112],"covering":[22,57,73,93,113],"number,":[23],"which":[24],"is":[25],"cardinality":[27],"smallest":[30],"sub-collection":[31],"\\mathcal{S}":[33],"whose":[35],"union":[36],"covers":[37],"universe":[39],"$.":[42],"This":[43],"paper":[44],"embraces":[45],"three":[46],"covering-related":[47],"problems":[48],"in":[49,95,103,115,127],"hierarchical":[50,96,116,129],"poset":[51],"spaces:":[52],"classic,":[54],"short":[56],"normal":[59],"codes.":[60],"In":[61],"first":[63],"two":[64],"problems,":[65],"classical":[67],"short-covering":[70],"ones,":[71],"numbers":[74],"are":[75,132],"studied":[76],"for":[77],"collections":[78],"R":[81,85,138],"$-balls":[82],"$-strips,":[86],"respectively.":[87],"We":[88],"prove":[89],"that":[90,131],"determining":[91],"number":[94,114],"spaces":[97],"depends":[98],"only":[99],"on":[100],"their":[101],"correspondents":[102],"Hamming":[105],"space.":[106],"It":[107],"allows":[108],"us":[109],"to":[110],"express":[111],"spaces.":[117],"Later":[118],"on,":[119],"characterize":[121],"all":[122],"\\mathcal{H}":[124],"$-normal":[125],"codes":[126],"binary":[128],"spaces,":[130],"distinctive":[134],"family":[135],"$-coverings.":[139]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}