{"id":"https://openalex.org/W3000042234","doi":"https://doi.org/10.37236/1480","title":"Resolving Triple Systems into Regular Configurations","display_name":"Resolving Triple Systems into Regular Configurations","publication_year":1999,"publication_date":"1999-11-22","ids":{"openalex":"https://openalex.org/W3000042234","doi":"https://doi.org/10.37236/1480","mag":"3000042234"},"language":"en","primary_location":{"id":"doi:10.37236/1480","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1480","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r2/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r2/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042503682","display_name":"Eric Mendelsohn","orcid":"https://orcid.org/0000-0002-2711-8995"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"E. Mendelsohn","raw_affiliation_strings":["Department of Mathematics, University of Toronto Toronto, ON M5S 3G3 CANADA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Toronto Toronto, ON M5S 3G3 CANADA","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032795071","display_name":"Gaetano Quattrocchi","orcid":null},"institutions":[{"id":"https://openalex.org/I39063666","display_name":"University of Catania","ror":"https://ror.org/03a64bh57","country_code":"IT","type":"education","lineage":["https://openalex.org/I39063666"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Quattrocchi","raw_affiliation_strings":["Dipartimento di Matematica, Universita' di Catania Catania, ITALIA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universita' di Catania Catania, ITALIA","institution_ids":["https://openalex.org/I39063666"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.3593614,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"7","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":0.9937000274658203,"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":0.9937000274658203,"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/T10849","display_name":"Finite Group Theory Research","score":0.9294000267982483,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.8482493162155151},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.7119584083557129},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6925225853919983},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.690995454788208},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5364919304847717},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4990732669830322},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.42168763279914856},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23788908123970032},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.06032872200012207}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8482493162155151},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.7119584083557129},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6925225853919983},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.690995454788208},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5364919304847717},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4990732669830322},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.42168763279914856},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23788908123970032},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.06032872200012207},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1480","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1480","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r2/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":false,"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:10.1.1.93.8428","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.93.8428","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_7/PDF/v7i1r2.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1480","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1480","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r2/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":false,"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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000042234.pdf","grobid_xml":"https://content.openalex.org/works/W3000042234.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W403078265","https://openalex.org/W1480085961","https://openalex.org/W1634651372","https://openalex.org/W1965142549","https://openalex.org/W1990217961","https://openalex.org/W2008651629","https://openalex.org/W2035580498","https://openalex.org/W2036952529","https://openalex.org/W2072764020","https://openalex.org/W2121231889","https://openalex.org/W2145952441","https://openalex.org/W4212917665","https://openalex.org/W4252832821","https://openalex.org/W4255583395","https://openalex.org/W6649797397","https://openalex.org/W6652486915","https://openalex.org/W6659891146","https://openalex.org/W6678260331","https://openalex.org/W6681613149"],"related_works":["https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W2951695430","https://openalex.org/W4256429076","https://openalex.org/W2012063272","https://openalex.org/W4300891849","https://openalex.org/W2318687609","https://openalex.org/W2348092930","https://openalex.org/W2499670206","https://openalex.org/W2188987556"],"abstract_inverted_index":{"A":[0,38,95],"$\\lambda-Triple\\":[1],"System(v)$,":[2],"or":[3,106,167,198],"a":[4,8,15,20,51,58,63,100,127,140,152],"$\\lambda":[5,206],"$\u2013$TS(V,\\cal{B})$,":[6],"is":[7,14,19,31,50,57,74,97,124,139],"pair":[9,30,52],"(V,":[10],"$\\cal{B}$)":[11],"where":[12,55],"V":[13,26],"set":[16,66,128],"and":[17,82,93,170,184,210,217],"$\\cal{B}$":[18],"subset":[21],"of":[22,25,36,60,62,79,129,133,151,176,182],"the":[23,137,203],"3-subsets":[24,61],"so":[27,68,118],"that":[28,69,119],"every":[29,70],"in":[32,72,75],"exactly":[33,76],"$\\lambda$":[34],"elements":[35,78],"$\\cal{B}$.":[37],"$regular\\":[39],"configuration$":[40],"on":[41,47,143,165],"p":[42,71],"points":[43,145],"with":[44],"regularity":[45],"$\\rho$":[46,77],"$l$":[48],"blocks":[49,169,197],"(P,${\\cal":[53,134],"L}$)":[54],"$\\cal{L}$":[56],"collection":[59],"(usually":[64],"small)":[65],"P":[67,73],"${\\cal":[80,110],"L}$,":[81],"$|{\\cal":[83],"L}|=l$.":[84],"The":[85],"Pasch":[86,204],"configuration":[87,102,138,205],"$(\\{0,1,2,3,4,5\\},\\{":[88],"012,035,245,134\\})$":[89],"has":[90],"p=6,":[91],"$l$=4,":[92],"$\\rho$=2.":[94],"$\\lambda$\u2013$TS(V,\\cal{B})$,":[96],"resolvable":[98],"into":[99,115],"regular":[101,161],"${\\Bbb":[103,107,163,172,193],"C}$=(P,${\\cal":[104],"L}$),":[105],"C}$\u2013resolvable,":[108],"if":[109],"B}$":[111],"can":[112],"be":[113],"partitioned":[114],"sets":[116],"$\\Pi_{i}$":[117],"for":[120,179,191,202],"each":[121,192],"i,":[122],"(V,$\\Pi_{i}$)":[123],"isomorphic":[125],"to":[126,148],"vertex":[130],"disjoint":[131],"copies":[132],"L}$).":[135],"If":[136],"single":[141],"block":[142],"three":[144],"this":[146,156],"corresponds":[147],"ordinary":[149],"resolvability":[150],"Triple":[153],"System.":[154],"In":[155],"paper":[157],"we":[158],"examine":[159],"all":[160],"configurations":[162],"C}$":[164,194],"6":[166],"fewer":[168],"construct":[171],"C}$\u2013resolvable":[173],"$\\lambda$\u2013Triple":[174],"Systems":[175],"order":[177],"v":[178,183],"many":[180],"values":[181],"$\\lambda$.":[185],"These":[186],"conditions":[187],"are":[188,215],"also":[189],"sufficient":[190],"having":[195],"4":[196],"fewer.":[199],"For":[200],"example":[201],"\\equiv":[207,212],"0":[208,213],"\\pmod{4}$":[209],"$v":[211],"\\pmod{6}$":[214],"necessary":[216],"sufficient.":[218]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
