{"id":"https://openalex.org/W2076621068","doi":"https://doi.org/10.1016/s0012-365x(98)00030-2","title":"The existence of perfect Mendelsohn designs with block size 7","display_name":"The existence of perfect Mendelsohn designs with block size 7","publication_year":1998,"publication_date":"1998-08-01","ids":{"openalex":"https://openalex.org/W2076621068","doi":"https://doi.org/10.1016/s0012-365x(98)00030-2","mag":"2076621068"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(98)00030-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0012-365x(98)00030-2","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0012365X98000302/pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://www.sciencedirect.com/science/article/pii/S0012365X98000302/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021994297","display_name":"R. Julian R. Abel","orcid":"https://orcid.org/0000-0002-3632-9612"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"R.J.R. Abel","raw_affiliation_strings":["School of Mathematics, University of New South Wales, Kensington, NSW 2033, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of New South Wales, Kensington, NSW 2033, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053962955","display_name":"F.E. Bennett","orcid":null},"institutions":[{"id":"https://openalex.org/I179301192","display_name":"Mount Saint Vincent University","ror":"https://ror.org/03g3p3b82","country_code":"CA","type":"education","lineage":["https://openalex.org/I179301192"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"F.E. Bennett","raw_affiliation_strings":["Department of Mathematics, Mt St Vincent University, Halifax, N.S., Canada B3M 2J6"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mt St Vincent University, Halifax, N.S., Canada B3M 2J6","institution_ids":["https://openalex.org/I179301192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021994297"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":{"value":3000,"currency":"USD","value_usd":3000},"fwci":1.4075,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.80549189,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"190","issue":"1-3","first_page":"1","last_page":"14"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998000264167786,"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":0.9998000264167786,"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/T11130","display_name":"Coding theory and cryptography","score":0.9805999994277954,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.8995318412780762},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7101954817771912},{"id":"https://openalex.org/keywords/mod","display_name":"Mod","score":0.6408854126930237},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5716108083724976},{"id":"https://openalex.org/keywords/block-size","display_name":"Block size","score":0.45988428592681885},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4564223289489746}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8995318412780762},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7101954817771912},{"id":"https://openalex.org/C29231244","wikidata":"https://www.wikidata.org/wiki/Q865493","display_name":"Mod","level":2,"score":0.6408854126930237},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5716108083724976},{"id":"https://openalex.org/C41431624","wikidata":"https://www.wikidata.org/wiki/Q1053357","display_name":"Block size","level":3,"score":0.45988428592681885},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4564223289489746},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0012-365x(98)00030-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0012-365x(98)00030-2","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0012365X98000302/pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s0012-365x(98)00030-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0012-365x(98)00030-2","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0012365X98000302/pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2076621068.pdf","grobid_xml":"https://content.openalex.org/works/W2076621068.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W110250935","https://openalex.org/W164275096","https://openalex.org/W1504945463","https://openalex.org/W1557001831","https://openalex.org/W1965142549","https://openalex.org/W1975012290","https://openalex.org/W1975150539","https://openalex.org/W1980562594","https://openalex.org/W1982062464","https://openalex.org/W1994566808","https://openalex.org/W2000317716","https://openalex.org/W2003319627","https://openalex.org/W2013330200","https://openalex.org/W2031498817","https://openalex.org/W2041994803","https://openalex.org/W2069903885","https://openalex.org/W2091310394","https://openalex.org/W2149235772","https://openalex.org/W2564166994","https://openalex.org/W2943241712","https://openalex.org/W3097586850","https://openalex.org/W6604491164","https://openalex.org/W6606659536"],"related_works":["https://openalex.org/W2077189200","https://openalex.org/W2393136772","https://openalex.org/W768788828","https://openalex.org/W4386229429","https://openalex.org/W2035025044","https://openalex.org/W3016449295","https://openalex.org/W53339341","https://openalex.org/W2484416673","https://openalex.org/W4362564423","https://openalex.org/W2123931954"],"abstract_inverted_index":{"Necessary":[0],"conditions":[1],"for":[2,51,71,94,107,113,127,136,141],"existence":[3,69],"of":[4,102],"a":[5],"(v,k,\u03bb)":[6],"perfect":[7],"Mendelsohn":[8],"design":[9],"(or":[10],"PMD)":[11],"are":[12,140],"v":[13,33,41,53,119,142,149],"\u2a7e":[14,42,54],"k":[15,25,72],"and":[16,40,50,64,78,89,111,131,148],"\u03bbv(v":[17],"\u2212":[18],"1)":[19],"\u2261":[20,34,58],"0":[21,35,47,59],"mod":[22,38,48,60],"k.":[23],"When":[24],"=":[26,73,76,109,120,129,143,150,153],"7,":[27,74],"this":[28],"condition":[29],"is":[30,122],"satisfied":[31],"if":[32],"or":[36],"1":[37,77,110,139],"7":[39,43,49,55],"when":[44,56],"\u03bb":[45,57,75,79,95,108,114,128,137,145,152],"\u2262":[46],"all":[52],"7.":[61,154],"Bennett,":[62],"Yin":[63],"Zhu":[65],"have":[66],"investigated":[67],"the":[68,92,99,123,132],"problem":[70],"even;":[80],"here":[81],"we":[82],"provide":[83],"several":[84],"improvements":[85],"on":[86],"their":[87],"results":[88],"also":[90],"investigate":[91],"situation":[93],"odd.":[96],"We":[97],"reduce":[98],"total":[100],"number":[101],"unknown":[103,125,134],"(v,7,\u03bb)-PMDs":[104],"to":[105],"36,31":[106],"5":[112],">":[115,138],"1.":[116],"In":[117],"particular,":[118],"294":[121],"largest":[124],"case":[126],"1,":[130],"only":[133],"cases":[135],"42,":[144],"\u2208":[146],"[2,3,5,9]":[147],"18,":[151]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}