{"id":"https://openalex.org/W2006109052","doi":"https://doi.org/10.1017/s0963548300002121","title":"Interval Packing and Covering in the Boolean Lattice","display_name":"Interval Packing and Covering in the Boolean Lattice","publication_year":1996,"publication_date":"1996-12-01","ids":{"openalex":"https://openalex.org/W2006109052","doi":"https://doi.org/10.1017/s0963548300002121","mag":"2006109052"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548300002121","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300002121","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025619790","display_name":"Konrad Engel","orcid":"https://orcid.org/0000-0002-9396-5332"},"institutions":[{"id":"https://openalex.org/I4665924","display_name":"University of Rostock","ror":"https://ror.org/03zdwsf69","country_code":"DE","type":"education","lineage":["https://openalex.org/I4665924"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Konrad Engel","raw_affiliation_strings":["Universit\u00e4t Rostock, FB Mathematik, 18051 Rostock, Germany","Universit\u00e4t Rostock, FB Mathematik, 18051, Rostock, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Rostock, FB Mathematik, 18051 Rostock, Germany","institution_ids":["https://openalex.org/I4665924"]},{"raw_affiliation_string":"Universit\u00e4t Rostock, FB Mathematik, 18051, Rostock, Germany","institution_ids":["https://openalex.org/I4665924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025619790"],"corresponding_institution_ids":["https://openalex.org/I4665924"],"apc_list":null,"apc_paid":null,"fwci":0.4905,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.66508521,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"5","issue":"4","first_page":"373","last_page":"384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/combinatorics","display_name":"Combinatorics","score":0.8544880747795105},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.7444393634796143},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7149177193641663},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6613171100616455},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5174927711486816},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.507443368434906},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4674317240715027},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.44635942578315735},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09644249081611633}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8544880747795105},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.7444393634796143},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7149177193641663},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6613171100616455},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5174927711486816},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.507443368434906},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4674317240715027},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.44635942578315735},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09644249081611633},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548300002121","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300002121","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1562813469","https://openalex.org/W2014669583","https://openalex.org/W2020421577","https://openalex.org/W2035697831","https://openalex.org/W2036554929","https://openalex.org/W2058848132","https://openalex.org/W2068795011","https://openalex.org/W2073847908","https://openalex.org/W2087567316","https://openalex.org/W2092907557","https://openalex.org/W2163322487","https://openalex.org/W7035911920"],"related_works":["https://openalex.org/W4376608589","https://openalex.org/W3138003926","https://openalex.org/W4300037846","https://openalex.org/W1630514295","https://openalex.org/W1537073411","https://openalex.org/W2963081352","https://openalex.org/W4376608938","https://openalex.org/W4288275998","https://openalex.org/W2472555608","https://openalex.org/W4214498971"],"abstract_inverted_index":{"Let":[0],"be":[1,131],"the":[2,7,35,39,73,77,78,86,90,110,115],"hypergraph":[3],"whose":[4,30],"points":[5,94],"are":[6,32],"subsets":[8],"X":[9,20,49,57,68],"of":[10,38,81,93],"[n]":[11],":=":[12],"{1,\u2026,":[13],"n":[14,46,121],"}":[15,54],"with":[16],"l":[17,25,60],"\u2264":[18,22],"|":[19,21,56,58,62,64],"u":[23,27,66],",":[24,28,61,67],"<":[26],"and":[29,85,103],"edges":[31],"intervals":[33],"in":[34],"Boolean":[36],"lattice":[37],"form":[40],"I":[41],"=":[42,59,65],"{":[43],"C":[44,51],"\u2286[":[45],"]":[47],":":[48],"\u2286":[50,52,69],"Y":[53,63,70],"where":[55,113],".We":[71],"study":[72],"matching":[74],"number":[75,80,88,92],"i.e.":[76,89],"maximum":[79],"pairwise":[82],"disjoint":[83],"edges,":[84],"covering":[87],"minimum":[91],"which":[95],"cover":[96],"all":[97],"edges.":[98],"We":[99],"prove":[100],"that":[101,104,120,139],"max":[102],"for":[105,114],"every":[106],"\u03b5":[107],">":[108],"0":[109],"inequalities":[111],"hold,":[112],"lower":[116],"bounds":[117],"we":[118,135],"suppose":[119],"is":[122],"not":[123],"too":[124],"small.":[125],"The":[126],"corresponding":[127],"fractional":[128],"numbers":[129],"can":[130],"determined":[132],"exactly.":[133],"Moreover,":[134],"show":[136],"by":[137],"construction":[138]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}