{"id":"https://openalex.org/W4376639538","doi":"https://doi.org/10.1145/3564246.3585149","title":"Linear Independence, Alternants, and Applications","display_name":"Linear Independence, Alternants, and Applications","publication_year":2023,"publication_date":"2023-05-16","ids":{"openalex":"https://openalex.org/W4376639538","doi":"https://doi.org/10.1145/3564246.3585149"},"language":"en","primary_location":{"id":"doi:10.1145/3564246.3585149","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3564246.3585149","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 55th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072953772","display_name":"Vishwas Bhargava","orcid":"https://orcid.org/0009-0005-7869-377X"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Vishwas Bhargava","raw_affiliation_strings":["University of Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020540233","display_name":"Shubhangi Saraf","orcid":"https://orcid.org/0009-0005-0874-2978"},"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":"Shubhangi Saraf","raw_affiliation_strings":["University of Toronto, Canada"],"affiliations":[{"raw_affiliation_string":"University of Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073965203","display_name":"Ilya Volkovich","orcid":"https://orcid.org/0000-0002-7616-0751"},"institutions":[{"id":"https://openalex.org/I103531236","display_name":"Boston College","ror":"https://ror.org/02n2fzt79","country_code":"US","type":"education","lineage":["https://openalex.org/I103531236"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ilya Volkovich","raw_affiliation_strings":["Boston College, USA"],"affiliations":[{"raw_affiliation_string":"Boston College, USA","institution_ids":["https://openalex.org/I103531236"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072953772"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.195,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51651233,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"441","last_page":"454"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9994999766349792,"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/independence","display_name":"Independence (probability theory)","score":0.8328360319137573},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.581856369972229},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.5008254051208496},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.45341596007347107},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43908724188804626},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4363013803958893},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1768662929534912}],"concepts":[{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.8328360319137573},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.581856369972229},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.5008254051208496},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.45341596007347107},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43908724188804626},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4363013803958893},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1768662929534912},{"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/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3564246.3585149","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3564246.3585149","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 55th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1508771701","https://openalex.org/W1532438862","https://openalex.org/W1838223085","https://openalex.org/W1968245619","https://openalex.org/W1974321539","https://openalex.org/W1976166549","https://openalex.org/W1991584875","https://openalex.org/W2003659538","https://openalex.org/W2015393485","https://openalex.org/W2015679114","https://openalex.org/W2026036943","https://openalex.org/W2026944800","https://openalex.org/W2034027554","https://openalex.org/W2050570613","https://openalex.org/W2059084795","https://openalex.org/W2065853216","https://openalex.org/W2080132708","https://openalex.org/W2104644213","https://openalex.org/W2136567612","https://openalex.org/W2139709458","https://openalex.org/W2142326730","https://openalex.org/W2147588253","https://openalex.org/W2148132824","https://openalex.org/W2155871167","https://openalex.org/W2177482211","https://openalex.org/W2181660280","https://openalex.org/W2498723049","https://openalex.org/W2508387244","https://openalex.org/W2753415005","https://openalex.org/W2771494552","https://openalex.org/W2803711344","https://openalex.org/W2963854229","https://openalex.org/W2996954275","https://openalex.org/W3090578916","https://openalex.org/W3106203092","https://openalex.org/W3136468253","https://openalex.org/W3140482674","https://openalex.org/W4205441565","https://openalex.org/W4233477278","https://openalex.org/W4298217050","https://openalex.org/W4299838326","https://openalex.org/W4388435690","https://openalex.org/W6743506739"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2768610039","https://openalex.org/W4308265086","https://openalex.org/W2949964783","https://openalex.org/W2106889256","https://openalex.org/W2801357573","https://openalex.org/W2735923117","https://openalex.org/W2115913661","https://openalex.org/W3168772390"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,19,49],"new":[3],"technique":[4],"for":[5,22],"analyzing":[6],"linear":[7],"independence":[8],"of":[9,13,54],"multivariate":[10],"polynomials.":[11],"One":[12],"our":[14],"main":[15],"technical":[16],"contributions":[17],"is":[18],"Small":[20],"Witness":[21],"Linear":[23],"Independence":[24],"(SWLI)":[25],"lemma":[26],"which":[27],"states":[28],"the":[29,32],"following.":[30],"If":[31],"polynomials":[33],"f1,f2,":[34,61],"\u2026,":[35,41,62],"fk":[36,63],"\u2208":[37],"F[X]":[38],"over":[39],"X={x1,":[40],"xn}":[42],"are":[43,64],"F-linearly":[44],"independent":[45],"then":[46],"there":[47],"exists":[48],"subset":[50],"S":[51],"\u2286":[52],"X":[53],"size":[55],"at":[56],"most":[57],"k\u22121":[58],"such":[59],"that":[60],"also":[65],"F(X\u2216":[66],"S)-linearly":[67],"independent.":[68]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}