{"id":"https://openalex.org/W186648476","doi":"https://doi.org/10.25596/jalc-2005-025","title":"Cubic and Semi-Cubic SQS-Skeins","display_name":"Cubic and Semi-Cubic SQS-Skeins","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W186648476","doi":"https://doi.org/10.25596/jalc-2005-025","mag":"186648476"},"language":"en","primary_location":{"id":"doi:10.25596/jalc-2005-025","is_oa":true,"landing_page_url":"https://doi.org/10.25596/jalc-2005-025","pdf_url":null,"source":{"id":"https://openalex.org/S7407052944","display_name":"Justus-Liebig-Universit\u00e4t Gie\u00dfen","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.25596/jalc-2005-025","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024405096","display_name":"M. H. Armanious","orcid":null},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Armanious, Magdi H.","raw_affiliation_strings":["Mathematics Department, Faculty of Science, Mansoura University, Mansora, Egypt#TAB#"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Mansoura University, Mansora, Egypt#TAB#","institution_ids":["https://openalex.org/I159247623"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024405096"],"corresponding_institution_ids":["https://openalex.org/I159247623"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01137721,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9939000010490417,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9929999709129333,"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/skein","display_name":"Skein","score":0.9259546399116516},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.8572520017623901},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7930009365081787},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6859011650085449},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5336245894432068},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41158774495124817},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19484207034111023},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08337563276290894}],"concepts":[{"id":"https://openalex.org/C194674032","wikidata":"https://www.wikidata.org/wiki/Q1142190","display_name":"Skein","level":2,"score":0.9259546399116516},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8572520017623901},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7930009365081787},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6859011650085449},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5336245894432068},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41158774495124817},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19484207034111023},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08337563276290894},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.25596/jalc-2005-025","is_oa":true,"landing_page_url":"https://doi.org/10.25596/jalc-2005-025","pdf_url":null,"source":{"id":"https://openalex.org/S7407052944","display_name":"Justus-Liebig-Universit\u00e4t Gie\u00dfen","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.25596/jalc-2005-025","is_oa":true,"landing_page_url":"https://doi.org/10.25596/jalc-2005-025","pdf_url":null,"source":{"id":"https://openalex.org/S7407052944","display_name":"Justus-Liebig-Universit\u00e4t Gie\u00dfen","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W4141857","https://openalex.org/W94221996","https://openalex.org/W306097772","https://openalex.org/W1987649928","https://openalex.org/W1998449276","https://openalex.org/W2006176601","https://openalex.org/W2032066269","https://openalex.org/W2037364571","https://openalex.org/W2059891919","https://openalex.org/W2318203863","https://openalex.org/W2327337282"],"related_works":["https://openalex.org/W2006176601","https://openalex.org/W2066794018","https://openalex.org/W2507909417","https://openalex.org/W2949229787","https://openalex.org/W2916450210","https://openalex.org/W3195658432","https://openalex.org/W1964012003","https://openalex.org/W2084397557","https://openalex.org/W2215040509","https://openalex.org/W177735987","https://openalex.org/W2996731093","https://openalex.org/W11591861","https://openalex.org/W2086291179","https://openalex.org/W2985745781","https://openalex.org/W306097772","https://openalex.org/W2038896524","https://openalex.org/W110553658","https://openalex.org/W2085228271","https://openalex.org/W3101365028","https://openalex.org/W1980795149"],"abstract_inverted_index":{"There":[0],"is":[1,17,33,55,79,83,131,162,189,195],"a":[2,64,76,93,104,132,163,177,190,229],"one":[3,5,184,239],"to":[4,19,58],"correspondence":[6],"between":[7],"quadruple":[8,15,52,67,150,192],"systems":[9,151],"and":[10,41],"SQS-skeins":[11,155],"(Quackenbush":[12],"1973).":[13],"A":[14],"system":[16,68,193],"said":[18],"be":[20,92],"subsystem":[21,50,65,158,197],"free,":[22],"if":[23,31,81],"it":[24,32,82],"contains":[25],"no":[26],"nontrivial":[27],"subsystems,":[28],"or":[29],"equivalently":[30],"generated":[34],"by":[35,108],"each":[36,139,244],"independent":[37],"4-element":[38],"subset.":[39],"Mendelsohn":[40],"Phelps":[42],"(1982)":[43],"have":[44],"given":[45],"several":[46],"recursive":[47],"constructions":[48],"of":[49,84,96,111,135,167,180,199,223,255],"free":[51,66,198],"systems.":[53],"It":[54],"more":[56],"convenient":[57],"call":[59],"the":[60,232,253],"SQS-skein":[61,78,95,106,134,165,179,222,246],"associated":[62,152],"with":[63,153],"cubic.":[69],"The":[70,149,213],"author":[71,214],"(1981)":[72,215],"has":[73,216],"proved":[74,217],"that":[75,129,174,187,218,243,250],"cubic":[77,164,221],"simple,":[80],"cardinality":[85,97,112,168,181,200,224],"$n":[86,122,146,225],"&gt;":[87,123,211,226],"8$.":[88,124],"Let":[89],"$(P_1;":[90],"q_1)$":[91],"simple":[94,105,133],"$n$.":[98],"In":[99],"this":[100],"paper,":[101],"we":[102,126,171],"construct":[103],"denoted":[107],"$(2\\otimes":[109],"P_1;q_{\\alpha,A})$":[110],"$2n$":[113],"for":[114,138,202],"any":[115,219],"$n\\equiv":[116,140],"2":[117,141],"\\or":[118,142,206],"4":[119,143,205],"(\\mod":[120,144,208],"6)$,":[121,145],"Consequently,":[125],"may":[127,185],"deduce":[128],"there":[130,161,175,188],"order":[136],"$n$":[137],"\\not=":[147],"4,8$.":[148],"these":[154],"are":[156],"not":[157,196],"free.":[159],"If":[160],"$(P_1;q_1)$":[166],"$n$,":[169],"then":[170],"will":[172],"prove":[173],"exists":[176],"semi-cubic":[178,191,245],"$2n$.":[182],"Accordingly,":[183],"say":[186],"which":[194],"$m$":[201],"all":[203,256],"$m\\equiv":[204],"8":[207],"12)$,":[209],"$m":[210],"16$.":[212],"finite":[220],"8$":[227],"generates":[228,247],"subvariety":[230,234],"covers":[231,252],"smallest":[233],"(the":[235],"Boolean":[236,257],"SQS-skeins).":[237],"Similarly,":[238],"can":[240],"directly":[241],"show":[242],"another":[248],"variety":[249,254],"also":[251],"SQS-skeins.":[258]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2016-06-24T00:00:00"}
