{"id":"https://openalex.org/W2103370605","doi":"https://doi.org/10.2478/v10037-008-0001-7","title":"The Vector Space of Subsets of a Set Based on Symmetric Difference","display_name":"The Vector Space of Subsets of a Set Based on Symmetric Difference","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2103370605","doi":"https://doi.org/10.2478/v10037-008-0001-7","mag":"2103370605"},"language":"en","primary_location":{"id":"doi:10.2478/v10037-008-0001-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0001-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0001-7","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/v10037-008-0001-7","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039051935","display_name":"Jesse Alama","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jesse Alama","raw_affiliation_strings":["Department of Philosophy Stanford University USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Philosophy Stanford University USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039051935"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":0.3019,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68697628,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"1","first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.8501999974250793,"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":0.8501999974250793,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.8170999884605408,"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.8003000020980835,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.835442304611206},{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.7845030426979065},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7373087406158447},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.663688063621521},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.6291482448577881},{"id":"https://openalex.org/keywords/normed-vector-space","display_name":"Normed vector space","score":0.5687451958656311},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5603872537612915},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5151432752609253},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4786840081214905},{"id":"https://openalex.org/keywords/disjoint-union","display_name":"Disjoint union (topology)","score":0.47578370571136475},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.472703218460083},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4668002724647522},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43438515067100525},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4283648729324341},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20943397283554077},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09141466021537781},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07463720440864563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.835442304611206},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.7845030426979065},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7373087406158447},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.663688063621521},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.6291482448577881},{"id":"https://openalex.org/C171739935","wikidata":"https://www.wikidata.org/wiki/Q726210","display_name":"Normed vector space","level":2,"score":0.5687451958656311},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5603872537612915},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5151432752609253},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4786840081214905},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.47578370571136475},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.472703218460083},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4668002724647522},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43438515067100525},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4283648729324341},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20943397283554077},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09141466021537781},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07463720440864563},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2478/v10037-008-0001-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0001-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0001-7","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.159.9985","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.159.9985","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mizar.org/fm/2008-16/pdf16-1/bspace.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:e0d18f7484164bdcb95a671464de927e","is_oa":false,"landing_page_url":"https://doaj.org/article/e0d18f7484164bdcb95a671464de927e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 16, Iss 1, Pp 1-5 (2008)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/20690","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/20690","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/v10037-008-0001-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0001-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0001-7","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2103370605.pdf","grobid_xml":"https://content.openalex.org/works/W2103370605.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W22141270","https://openalex.org/W180239714","https://openalex.org/W192809544","https://openalex.org/W260340778","https://openalex.org/W2105559527","https://openalex.org/W2112849387","https://openalex.org/W2131545826","https://openalex.org/W2138253682","https://openalex.org/W2145706675","https://openalex.org/W2150348213","https://openalex.org/W2153830101","https://openalex.org/W2158768890","https://openalex.org/W2159772409","https://openalex.org/W2163641194","https://openalex.org/W2167846685","https://openalex.org/W2167862310","https://openalex.org/W2547540153","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4245268118","https://openalex.org/W4232341271","https://openalex.org/W4382600406","https://openalex.org/W2617085105","https://openalex.org/W928614972","https://openalex.org/W4231104074","https://openalex.org/W4250540213","https://openalex.org/W2374594895","https://openalex.org/W3187046455","https://openalex.org/W2092976320"],"abstract_inverted_index":{"The":[0],"Vector":[1],"Space":[2],"of":[3,5,18,66],"Subsets":[4],"a":[6,21],"Set":[7],"Based":[8],"on":[9],"Symmetric":[10],"DifferenceFor":[11],"each":[12],"set":[13,17],"X,":[14],"the":[15,25,51],"power":[16],"X":[19],"forms":[20],"vector":[22,40],"space":[23],"over":[24],"field":[26,30],"Z2":[27],"(the":[28],"two-element":[29],"{0,":[31],"1}":[32],"with":[33],"addition":[34,41],"and":[35,45],"multiplication":[36,47],"done":[37],"modulo":[38],"2):":[39],"is":[42,48],"disjoint":[43],"union,":[44],"scalar":[46],"defined":[49],"by":[50],"two":[52],"equations":[53],"(1":[54],"\u00b7":[55,59],"x:=":[56],"x,":[57],"0":[58],"x":[60,65],":=":[61],"\u2205":[62],"for":[63,72],"subsets":[64],"X).":[67],"See":[68],"[10],":[69],"Exercise":[70],"2.K,":[71],"more":[73],"information.MML":[74],"identifier:":[75],"BSPACE,":[76],"version:":[77],"7.8.05":[78],"4.89.993":[79]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-03T07:22:36.454288","created_date":"2025-10-10T00:00:00"}
