{"id":"https://openalex.org/W2963868215","doi":"https://doi.org/10.37236/4874","title":"Heffter Arrays and Biembedding Graphs on Surfaces","display_name":"Heffter Arrays and Biembedding Graphs on Surfaces","publication_year":2015,"publication_date":"2015-03-23","ids":{"openalex":"https://openalex.org/W2963868215","doi":"https://doi.org/10.37236/4874","mag":"2963868215"},"language":"en","primary_location":{"id":"doi:10.37236/4874","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4874","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p74/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v22i1p74/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061516469","display_name":"Dan Archdeacon","orcid":null},"institutions":[{"id":"https://openalex.org/I111236770","display_name":"University of Vermont","ror":"https://ror.org/0155zta11","country_code":"US","type":"education","lineage":["https://openalex.org/I111236770"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dan Archdeacon","raw_affiliation_strings":["The University of Vermont"],"affiliations":[{"raw_affiliation_string":"The University of Vermont","institution_ids":["https://openalex.org/I111236770"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061516469"],"corresponding_institution_ids":["https://openalex.org/I111236770"],"apc_list":null,"apc_paid":null,"fwci":1.7756,"has_fulltext":true,"cited_by_count":47,"citation_normalized_percentile":{"value":0.87026059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"22","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9835000038146973,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9804999828338623,"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/mathematics","display_name":"Mathematics","score":0.7821066379547119},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7699193954467773},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4989931583404541},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.466705322265625},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.46418896317481995},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.426751971244812},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.42321497201919556},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11689901351928711}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7821066379547119},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7699193954467773},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4989931583404541},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.466705322265625},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.46418896317481995},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.426751971244812},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42321497201919556},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11689901351928711},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/4874","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4874","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p74/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/4874","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4874","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p74/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2963868215.pdf","grobid_xml":"https://content.openalex.org/works/W2963868215.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1558273801","https://openalex.org/W1635410918","https://openalex.org/W1889896615","https://openalex.org/W1952453666","https://openalex.org/W1963619425","https://openalex.org/W1964422212","https://openalex.org/W1986333526","https://openalex.org/W2007349912","https://openalex.org/W2011976580","https://openalex.org/W2034000616","https://openalex.org/W2054779640","https://openalex.org/W2088320806","https://openalex.org/W2358490219","https://openalex.org/W6603109425"],"related_works":["https://openalex.org/W2378076731","https://openalex.org/W4286888643","https://openalex.org/W3210795196","https://openalex.org/W2088988140","https://openalex.org/W2803103875","https://openalex.org/W2103019253","https://openalex.org/W2951529875","https://openalex.org/W2391453316","https://openalex.org/W2297768894","https://openalex.org/W1988064119"],"abstract_inverted_index":{"A":[0],"Heffter":[1,42,102],"array":[2],"is":[3],"an":[4],"$m":[5],"\\times":[6],"n$":[7],"matrix":[8],"with":[9,104],"nonzero":[10,33],"entries":[11],"from":[12],"$\\mathbb{Z}_{2mn+1}$":[13],"such":[14],"that":[15,71],"i)":[16],"every":[17],"row":[18],"and":[19,24,113],"column":[20],"sum":[21],"to":[22,48,64],"0,":[23],"ii)":[25],"exactly":[26],"one":[27],"of":[28,32,93,119],"each":[29,83],"pair":[30],"$\\{x,-x\\}$":[31],"elements":[34],"appears":[35],"in":[36,53,117],"the":[37,59,66,72],"array.":[38],"We":[39,97],"construct":[40],"some":[41,99],"arrays.":[43],"These":[44,90],"arrays":[45,103],"are":[46,62],"used":[47,52,63],"build":[49],"current":[50,60],"graphs":[51,61],"topological":[54],"graph":[55,68],"theory.":[56],"In":[57],"turn,":[58],"embed":[65],"complete":[67,111],"$K_{2mn+1}$":[69],"so":[70],"faces":[73],"can":[74],"be":[75],"2-colored,":[76],"called":[77],"a":[78,87],"biembedding.":[79],"Under":[80],"certain":[81],"conditions":[82],"color":[84],"class":[85],"forms":[86],"cycle":[88],"system.":[89],"generalize":[91],"biembeddings":[92],"Steiner":[94],"triple":[95],"systems.":[96],"discuss":[98],"variations":[100],"including":[101],"empty":[105],"cells,":[106],"embeddings":[107],"on":[108],"nonorientable":[109],"surfaces,":[110],"multigraphs,":[112],"using":[114],"integer":[115],"arithmetic":[116],"place":[118],"modular":[120],"arithmetic.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
