{"id":"https://openalex.org/W1974396706","doi":"https://doi.org/10.1016/s0012-365x(99)00134-x","title":"An n to 2n embedding of incomplete idempotent latin squares for small values of n","display_name":"An n to 2n embedding of incomplete idempotent latin squares for small values of n","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1974396706","doi":"https://doi.org/10.1016/s0012-365x(99)00134-x","mag":"1974396706"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(99)00134-x","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)00134-x","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"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":"Discrete Mathematics","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/A5041073099","display_name":"Christine Grant","orcid":"https://orcid.org/0000-0002-2303-0523"},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Grant","raw_affiliation_strings":["Department of Discrete and Statistical Sciences, 120 Mathematics Annex, Auburn University, Auburn, AL 36849-5307, USA"],"affiliations":[{"raw_affiliation_string":"Department of Discrete and Statistical Sciences, 120 Mathematics Annex, Auburn University, Auburn, AL 36849-5307, USA","institution_ids":["https://openalex.org/I82497590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091292004","display_name":"C. A. Rodger","orcid":null},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C.A. Rodger","raw_affiliation_strings":["Department of Discrete and Statistical Sciences, 120 Mathematics Annex, Auburn University, Auburn, AL 36849-5307, USA"],"affiliations":[{"raw_affiliation_string":"Department of Discrete and Statistical Sciences, 120 Mathematics Annex, Auburn University, Auburn, AL 36849-5307, USA","institution_ids":["https://openalex.org/I82497590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091292004"],"corresponding_institution_ids":["https://openalex.org/I82497590"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.0756149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"211","issue":"1-3","first_page":"53","last_page":"74"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9399999976158142,"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/latin-square","display_name":"Latin square","score":0.9566315412521362},{"id":"https://openalex.org/keywords/idempotence","display_name":"Idempotence","score":0.9415086507797241},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8701449632644653},{"id":"https://openalex.org/keywords/idempotent-matrix","display_name":"Idempotent matrix","score":0.7324674129486084},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6936600208282471},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6898590326309204},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6237229108810425},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.4733208119869232},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41987860202789307},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06044888496398926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05160391330718994}],"concepts":[{"id":"https://openalex.org/C158887663","wikidata":"https://www.wikidata.org/wiki/Q679367","display_name":"Latin square","level":4,"score":0.9566315412521362},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.9415086507797241},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8701449632644653},{"id":"https://openalex.org/C33375987","wikidata":"https://www.wikidata.org/wiki/Q3751720","display_name":"Idempotent matrix","level":3,"score":0.7324674129486084},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6936600208282471},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6898590326309204},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6237229108810425},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.4733208119869232},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41987860202789307},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06044888496398926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05160391330718994},{"id":"https://openalex.org/C70262065","wikidata":"https://www.wikidata.org/wiki/Q427652","display_name":"Rumen","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C100544194","wikidata":"https://www.wikidata.org/wiki/Q41760","display_name":"Fermentation","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C31903555","wikidata":"https://www.wikidata.org/wiki/Q1637030","display_name":"Food science","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0012-365x(99)00134-x","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)00134-x","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"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":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1436880534","https://openalex.org/W1896273107","https://openalex.org/W2003670649","https://openalex.org/W2026686068","https://openalex.org/W2037688303","https://openalex.org/W2052430893","https://openalex.org/W4238841606"],"related_works":["https://openalex.org/W4212917286","https://openalex.org/W2379578187","https://openalex.org/W1979565872","https://openalex.org/W2357199145","https://openalex.org/W2393613245","https://openalex.org/W1974396706","https://openalex.org/W2016077538","https://openalex.org/W2090259579","https://openalex.org/W1896273107","https://openalex.org/W2094401668"],"abstract_inverted_index":null,"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}