{"id":"https://openalex.org/W1612117521","doi":"https://doi.org/10.37236/1967","title":"Permanents of Hessenberg (0,1)-matrices","display_name":"Permanents of Hessenberg (0,1)-matrices","publication_year":2005,"publication_date":"2005-12-13","ids":{"openalex":"https://openalex.org/W1612117521","doi":"https://doi.org/10.37236/1967","mag":"1612117521"},"language":"en","primary_location":{"id":"doi:10.37236/1967","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1967","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r70/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r70/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064094814","display_name":"D.D. Olesky","orcid":null},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"D. D. Olesky","raw_affiliation_strings":["Department of Computer Science University of Victoria Victoria, BC V8W 3P6 Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Victoria Victoria, BC V8W 3P6 Canada","institution_ids":["https://openalex.org/I212119943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004584423","display_name":"Bryan L. Shader","orcid":"https://orcid.org/0000-0002-4407-4840"},"institutions":[{"id":"https://openalex.org/I12834331","display_name":"University of Wyoming","ror":"https://ror.org/01485tq96","country_code":"US","type":"education","lineage":["https://openalex.org/I12834331"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bryan Shader","raw_affiliation_strings":["Department of Mathematics University of Wyoming Laramie, WY 82071"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Wyoming Laramie, WY 82071","institution_ids":["https://openalex.org/I12834331"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049802779","display_name":"P. van den Driessche","orcid":"https://orcid.org/0000-0003-1485-8326"},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"P. Van den Driessche","raw_affiliation_strings":["Department of Mathematics University of Victoria Victoria, BC V8W 3P4 Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Victoria Victoria, BC V8W 3P4 Canada","institution_ids":["https://openalex.org/I212119943"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064094814"],"corresponding_institution_ids":["https://openalex.org/I212119943"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07954109,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.996999979019165,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.996999979019165,"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":0.9812999963760376,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9693999886512756,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7407751083374023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7162129878997803},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.591234028339386},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.2731037139892578}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7407751083374023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7162129878997803},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.591234028339386},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.2731037139892578},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1967","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1967","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r70/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.83.1192","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.1192","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_12/PDF/v12i1r70.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1967","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1967","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r70/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1612117521.pdf","grobid_xml":"https://content.openalex.org/works/W1612117521.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1568175246","https://openalex.org/W1985359679","https://openalex.org/W2027125203","https://openalex.org/W2052889187","https://openalex.org/W4299798129"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Let":[0],"$P\\left(":[1,37,56],"m,n\\right)":[2,38,57],"$":[3,39,58],"denote":[4],"the":[5,52,78],"maximum":[6,29,79],"permanent":[7],"of":[8,55,81],"an":[9,84],"$n$-by-$n$":[10,85],"lower":[11],"Hessenberg":[12,86],"$(0,1)":[13],"$-matrix":[14],"with":[15],"$m$":[16],"entries":[17],"equal":[18],"to":[19,50],"1.":[20],"A":[21],"\"staircased\"":[22],"structure":[23,43],"for":[24,35,59,66],"some":[25],"matrices":[26],"achieving":[27],"this":[28],"is":[30,77],"obtained,":[31],"and":[32,44,65],"recursive":[33],"formulas":[34],"computing":[36],"are":[40,48],"given.":[41],"This":[42],"results":[45],"about":[46],"permanents":[47],"used":[49],"determine":[51],"exact":[53],"values":[54],"$n":[60],"\\leq":[61,63,71,73],"m":[62,72],"8n/3$":[64],"all":[67],"$\\hbox{nnz}(H_n)-\\hbox{nnz}(H_{\\lfloor":[68],"n/2":[69],"\\rfloor})":[70],"\\hbox{nnz}(H_n)$,":[74],"where":[75],"$\\hbox{nnz}(H_n)=(n^2+3n-2)/2$":[76],"number":[80],"ones":[82],"in":[83],"$(0,1)$-matrix.":[87]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}