{"id":"https://openalex.org/W2964226640","doi":"https://doi.org/10.4086/toc.2015.v011a011","title":"","display_name":"","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2964226640","doi":"https://doi.org/10.4086/toc.2015.v011a011","mag":"2964226640"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2015.v011a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2015.v011a011","pdf_url":"http://www.theoryofcomputing.org/articles/v011a011/v011a011.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://www.theoryofcomputing.org/articles/v011a011/v011a011.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068623131","display_name":"J. M. Landsberg","orcid":"https://orcid.org/0000-0001-9880-1815"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Joseph M. Landsberg","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060402032","display_name":"Giorgio Ottaviani","orcid":"https://orcid.org/0000-0003-1275-1189"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giorgio Ottaviani","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068623131"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5376,"has_fulltext":true,"cited_by_count":66,"citation_normalized_percentile":{"value":0.94194757,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"11","issue":"1","first_page":"285","last_page":"298"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9965999722480774,"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"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/computer-science","display_name":"Computer science","score":0.45071256160736084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35925549268722534}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45071256160736084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35925549268722534}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4086/toc.2015.v011a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2015.v011a011","pdf_url":"http://www.theoryofcomputing.org/articles/v011a011/v011a011.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},{"id":"pmh:oai:flore.unifi.it:2158/1038824","is_oa":true,"landing_page_url":"http://hdl.handle.net/2158/1038824","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.4086/toc.2015.v011a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2015.v011a011","pdf_url":"http://www.theoryofcomputing.org/articles/v011a011/v011a011.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2573627744","display_name":null,"funder_award_id":"GNSAGA","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G2869503544","display_name":"Anlaytic Geometry and Representation Theory","funder_award_id":"1006353","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5253175522","display_name":null,"funder_award_id":"DMS-1006353","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334045","display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2964226640.pdf","grobid_xml":"https://content.openalex.org/works/W2964226640.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1527197079","https://openalex.org/W1531014798","https://openalex.org/W1561337879","https://openalex.org/W1576873230","https://openalex.org/W1737655677","https://openalex.org/W1986127216","https://openalex.org/W1993592754","https://openalex.org/W1997237738","https://openalex.org/W2004948173","https://openalex.org/W2007666181","https://openalex.org/W2023724794","https://openalex.org/W2035476608","https://openalex.org/W2066723539","https://openalex.org/W2074207216","https://openalex.org/W2079910744","https://openalex.org/W2084313768","https://openalex.org/W2094090625","https://openalex.org/W2102892751","https://openalex.org/W2120248756","https://openalex.org/W2199137233","https://openalex.org/W2405068759","https://openalex.org/W2577623060","https://openalex.org/W2964247109","https://openalex.org/W3149756008","https://openalex.org/W4244313943","https://openalex.org/W4251659063","https://openalex.org/W4255286089","https://openalex.org/W4293765205"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"The":[0,63],"border":[1,30,76],"rank":[2,31,77],"of":[3,16,52,74,87],"the":[4,29,43],"matrix":[5,92],"multiplication":[6,93],"operator":[7],"for":[8,59,84],"n":[9,10,61],"matrices":[11],"is":[12,32],"a":[13],"standard":[14],"measure":[15],"its":[17],"complexity.":[18],"Using":[19],"techniques":[20],"from":[21],"algebraic":[22],"geometry":[23],"and":[24],"representation":[25],"theory,":[26],"we":[27],"show":[28],"at":[33],"least":[34],"2n":[35],"2":[36,54],"-n.":[37],"Our":[38],"bounds":[39,64],"are":[40,65],"better":[41],"than":[42],"previous":[44],"lower":[45],"bound":[46],"(due":[47],"to":[48,95],"Lickteig":[49],"in":[50],"1985)":[51],"3n":[53],"/2":[55],"+":[56],"n/2":[57],"-1":[58],"all":[60],"3.":[62],"obtained":[66],"by":[67],"finding":[68],"new":[69,82],"equations":[70,83],"that":[71,91],"bilinear":[72],"maps":[73],"small":[75],"must":[78],"satisfy,":[79],"i.":[80],"e.,":[81],"secant":[85],"varieties":[86],"triple":[88],"Segre":[89],"products,":[90],"fails":[94],"satisfy.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2019-07-30T00:00:00"}