{"id":"https://openalex.org/W7213944786","doi":"https://doi.org/10.48550/arxiv.2609.21874","title":"Boolean building set arrangements","display_name":"Boolean building set arrangements","publication_year":2026,"publication_date":"2026-09-18","ids":{"openalex":"https://openalex.org/W7213944786","doi":"https://doi.org/10.48550/arxiv.2609.21874"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.21874","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21874","pdf_url":"https://arxiv.org/pdf/2609.21874","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.21874","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092467498","display_name":"Leonie M\u00fchlherr","orcid":"https://orcid.org/0009-0000-9900-7242","observed_orcids":["https://orcid.org/0009-0000-9900-7242"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M\u00fchlherr, Leonie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5119979159","display_name":"Sven Wiesner","orcid":"https://orcid.org/0009-0007-8845-4320","observed_orcids":["https://orcid.org/0009-0007-8845-4320"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wiesner, Sven","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9911999702453613,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9911999702453613,"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"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.0026000000070780516,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.0010999999940395355,"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/free-arrangements","display_name":"free arrangements","score":0.8220000267028809},{"id":"https://openalex.org/keywords/hypergraphs","display_name":"hypergraphs","score":0.45899999141693115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6671000123023987},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6015999913215637},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5759999752044678},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49239999055862427},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4893999993801117},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4546000063419342},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4465999901294708},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.43389999866485596},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4262999892234802},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.39559999108314514},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.38280001282691956},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37290000915527344},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.2773999869823456},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26499998569488525},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2639000117778778},{"id":"https://openalex.org/C146867743","wikidata":"https://www.wikidata.org/wiki/Q4669959","display_name":"Abstract simplicial complex","level":3,"score":0.25870001316070557},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.25540000200271606}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.21874","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21874","pdf_url":"https://arxiv.org/pdf/2609.21874","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.21874","doi":"https://doi.org/10.48550/arxiv.2609.21874","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.21874","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.21874","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21874","pdf_url":"https://arxiv.org/pdf/2609.21874","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213944786.pdf","grobid_xml":"https://content.openalex.org/works/W7213944786.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W377884864","https://openalex.org/W1982284001","https://openalex.org/W2026554022","https://openalex.org/W2039415399","https://openalex.org/W2044629946","https://openalex.org/W2085821474","https://openalex.org/W2130848020","https://openalex.org/W2207221396","https://openalex.org/W2610708034","https://openalex.org/W2735391782","https://openalex.org/W2964329608","https://openalex.org/W3037057336","https://openalex.org/W3198689540","https://openalex.org/W4392677766","https://openalex.org/W4415188170","https://openalex.org/W7131655587"],"related_works":["https://openalex.org/W2873776808","https://openalex.org/W4389670971","https://openalex.org/W7131655587","https://openalex.org/W4415188170","https://openalex.org/W4381573458","https://openalex.org/W7087798386","https://openalex.org/W4392866647","https://openalex.org/W2964450952","https://openalex.org/W2303767779","https://openalex.org/W1622091537"],"abstract_inverted_index":{"In":[0],"this":[1,104],"article,":[2],"we":[3,67],"generalize":[4],"the":[5,33,43,63,84,88,94],"notion":[6],"of":[7,19,35,45,72,87,96],"connected":[8,37,47],"subgraph":[9,48],"arrangements,":[10,49],"established":[11],"by":[12,16,75],"Cuntz":[13],"and":[14,98],"K\u00fchne":[15],"allowing":[17],"edges":[18],"cardinality":[20],"greater":[21],"than":[22,42],"two,":[23],"with":[24,78],"a":[25,54,69],"focus":[26],"on":[27],"local":[28],"properties.":[29],"We":[30,82],"show":[31],"that":[32,51,59],"class":[34,44],"free":[36,46],"hypersubgraph":[38],"arrangements":[39,74,102],"is":[40],"larger":[41],"but":[50],"there":[52],"exists":[53],"necessary":[55],"condition":[56],"for":[57],"freeness":[58],"refers":[60],"back":[61],"to":[62,93],"graphic":[64],"case.":[65],"Furthermore,":[66],"obtain":[68],"unique":[70],"description":[71],"these":[73],"associating":[76],"them":[77],"Boolean":[79],"building":[80,89],"sets.":[81],"study":[83],"nested":[85],"complex":[86],"set":[90],"in":[91],"relation":[92],"lattice":[95],"intersections,":[97],"characterize":[99],"all":[100],"simplicial":[101],"within":[103],"new":[105],"class.":[106]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-22T00:00:00"}