{"id":"https://openalex.org/W1995648919","doi":"https://doi.org/10.1016/s0195-6698(81)80016-9","title":"On Haber's Minimum Term Rank Formula","display_name":"On Haber's Minimum Term Rank Formula","publication_year":1981,"publication_date":"1981-03-01","ids":{"openalex":"https://openalex.org/W1995648919","doi":"https://doi.org/10.1016/s0195-6698(81)80016-9","mag":"1995648919"},"language":"en","primary_location":{"id":"doi:10.1016/s0195-6698(81)80016-9","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0195-6698(81)80016-9","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0195669881800169/pdf","source":{"id":"https://openalex.org/S204851967","display_name":"European Journal of Combinatorics","issn_l":"0195-6698","issn":["0195-6698","1095-9971"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.sciencedirect.com/science/article/pii/S0195669881800169/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061925223","display_name":"Richard A. Brualdi","orcid":"https://orcid.org/0000-0002-0841-7375"},"institutions":[{"id":"https://openalex.org/I1304256225","display_name":"University of Wisconsin System","ror":"https://ror.org/03ydkyb10","country_code":"US","type":"education","lineage":["https://openalex.org/I1304256225"]},{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Richard A. Brualdi","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, U.S.A","Department of Mathematics, University of Wisconsin Madison, Wisconsin 53706, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, U.S.A","institution_ids":["https://openalex.org/I1304256225","https://openalex.org/I135310074"]},{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin Madison, Wisconsin 53706, U.S.A","institution_ids":["https://openalex.org/I1304256225","https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061925223"],"corresponding_institution_ids":["https://openalex.org/I1304256225","https://openalex.org/I135310074"],"apc_list":{"value":3560,"currency":"USD","value_usd":3560},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.11721274,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"1","first_page":"17","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9833999872207642,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9728000164031982,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9112377166748047},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.7900444269180298},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7785879969596863},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6893295049667358},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.607479453086853},{"id":"https://openalex.org/keywords/column","display_name":"Column (typography)","score":0.5135881900787354},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07972300052642822}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9112377166748047},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.7900444269180298},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7785879969596863},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6893295049667358},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.607479453086853},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.5135881900787354},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07972300052642822},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0195-6698(81)80016-9","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0195-6698(81)80016-9","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0195669881800169/pdf","source":{"id":"https://openalex.org/S204851967","display_name":"European Journal of Combinatorics","issn_l":"0195-6698","issn":["0195-6698","1095-9971"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s0195-6698(81)80016-9","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0195-6698(81)80016-9","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0195669881800169/pdf","source":{"id":"https://openalex.org/S204851967","display_name":"European Journal of Combinatorics","issn_l":"0195-6698","issn":["0195-6698","1095-9971"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1995648919.pdf","grobid_xml":"https://content.openalex.org/works/W1995648919.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1969019522","https://openalex.org/W2323826585","https://openalex.org/W2331984355","https://openalex.org/W2695288266","https://openalex.org/W6740465696","https://openalex.org/W6824878413"],"related_works":["https://openalex.org/W1585007175","https://openalex.org/W2382521049","https://openalex.org/W2144385241","https://openalex.org/W2165950148","https://openalex.org/W4253593777","https://openalex.org/W2951497643","https://openalex.org/W2181722423","https://openalex.org/W4300101996","https://openalex.org/W3101625811","https://openalex.org/W2347222412"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
