{"id":"https://openalex.org/W2512432573","doi":"https://doi.org/10.1090/mcom/3284","title":"The method of shifted partial derivatives cannot separate the permanent from the determinant","display_name":"The method of shifted partial derivatives cannot separate the permanent from the determinant","publication_year":2017,"publication_date":"2017-06-08","ids":{"openalex":"https://openalex.org/W2512432573","doi":"https://doi.org/10.1090/mcom/3284","mag":"2512432573"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3284","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3284","pdf_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03284-1/S0025-5718-2017-03284-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03284-1/S0025-5718-2017-03284-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083692440","display_name":"Klim Efremenko","orcid":"https://orcid.org/0000-0003-3280-3927"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Klim Efremenko","raw_affiliation_strings":["Computer Science Department, Ben-Gurion University, Beer-Sheva, 84105 Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, Ben-Gurion University, Beer-Sheva, 84105 Israel","institution_ids":["https://openalex.org/I124227911"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068623131","display_name":"J. M. Landsberg","orcid":"https://orcid.org/0000-0001-9880-1815"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Landsberg","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, Texas 77843","Department of Mathematics, Texas A&M University, College Station, Texas 77843,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Texas 77843","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Texas 77843,","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038521689","display_name":"Hal Schenck","orcid":"https://orcid.org/0000-0002-1692-7500"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hal Schenck","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, Iowa 50011","Department of Mathematics, Iowa State University, Ames, Iowa 50011#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, Iowa 50011","institution_ids":["https://openalex.org/I173911158"]},{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, Iowa 50011#TAB#","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056139547","display_name":"Jerzy Weyman","orcid":"https://orcid.org/0000-0003-1923-0060"},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jerzy Weyman","raw_affiliation_strings":["Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269","Department of Mathematics , University of Connecticut , Storrs, Connecticut, 06269"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269","institution_ids":["https://openalex.org/I140172145"]},{"raw_affiliation_string":"Department of Mathematics , University of Connecticut , Storrs, Connecticut, 06269","institution_ids":["https://openalex.org/I140172145"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8484,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68003243,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"87","issue":"312","first_page":"2037","last_page":"2045"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/mathematics","display_name":"Mathematics","score":0.7044169306755066},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6919668912887573},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6380072832107544},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5953347086906433},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5070700645446777},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48003971576690674},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.4138086140155792},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25534799695014954},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.052577465772628784}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7044169306755066},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6919668912887573},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6380072832107544},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5953347086906433},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5070700645446777},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48003971576690674},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.4138086140155792},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25534799695014954},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.052577465772628784},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/3284","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3284","pdf_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03284-1/S0025-5718-2017-03284-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1609.02103","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.02103","pdf_url":"https://arxiv.org/pdf/1609.02103","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2512432573","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1609.02103.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1609.02103","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1609.02103","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"}],"best_oa_location":{"id":"doi:10.1090/mcom/3284","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3284","pdf_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03284-1/S0025-5718-2017-03284-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6922647057","display_name":null,"funder_award_id":"DMS-1312071","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7134197523","display_name":null,"funder_award_id":"DMS 1400740","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7953828331","display_name":null,"funder_award_id":"DMS 1405348","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1986127216","https://openalex.org/W2016576580","https://openalex.org/W2044352141","https://openalex.org/W2056881179","https://openalex.org/W2084050956","https://openalex.org/W2093103267","https://openalex.org/W2094107417","https://openalex.org/W2102018247","https://openalex.org/W2128510017","https://openalex.org/W2130566259","https://openalex.org/W2170831059","https://openalex.org/W2405068759","https://openalex.org/W2950754397","https://openalex.org/W2951580623","https://openalex.org/W6600555029","https://openalex.org/W6685152964"],"related_works":["https://openalex.org/W2962754399","https://openalex.org/W3012485420","https://openalex.org/W2951171881","https://openalex.org/W3200234314","https://openalex.org/W3005867397","https://openalex.org/W2152247860","https://openalex.org/W1968460700","https://openalex.org/W2949992887","https://openalex.org/W2278314150","https://openalex.org/W2146491975","https://openalex.org/W2007456941","https://openalex.org/W2048440529","https://openalex.org/W1993072318","https://openalex.org/W2091075857","https://openalex.org/W1984649098","https://openalex.org/W1575889851","https://openalex.org/W2018223420","https://openalex.org/W2952384725","https://openalex.org/W2571352639","https://openalex.org/W2051946902"],"abstract_inverted_index":{"The":[0],"method":[1,72],"of":[2,36,38,59,175,248,262,290],"shifted":[3,287],"partial":[4,288],"derivatives":[5,289],"introduced":[6],"A.":[7],"Gupta":[8],"et":[9],"al.":[10],"[":[11,28,271],"<italic>Approaching":[12,272],"the":[13,34,57,66,77,142,176,249,260,273,286,291],"chasm":[14,274],"at":[15,275],"depth":[16,60,276],"four</italic>":[17,277],",":[18,42,278],"IEEE":[19,279],"Comp.":[20,280],"Soc.,":[21,281],"2013,":[22,282],"pp.":[23,283],"65-73]":[24,284],"and":[25,265],"N.":[26],"Kayal":[27],"<italic>An":[29],"exponential":[30],"lower":[31,54,257,267],"bound":[32,55,258,268],"for":[33],"sum":[35],"powers":[37],"bounded":[39],"degree":[40],"polynomials</italic>":[41],"ECCC":[43],"19,":[44],"2010,":[45],"p.":[46],"81],":[47],"was":[48],"used":[49],"to":[50,64],"prove":[51,75],"a":[52,256,266],"super-polynomial":[53],"on":[56,244,259],"size":[58],"four":[61],"circuits":[62],"needed":[63],"compute":[65],"permanent.":[67],"We":[68],"show":[69],"that":[70,76],"this":[71],"alone":[73],"cannot":[74,138],"padded":[78],"permanent":[79],"<inline-formula":[80,143,178,210],"content-type=\"math/mathml\">":[81,144,179,211],"<mml:math":[82,145,180,212],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[83,146,181,213],"alttext=\"script":[84],"l":[85],"Superscript":[86],"n":[87,152],"minus":[88],"m":[89,98,217],"Baseline":[90],"normal":[91,93,95,97,184,186],"p":[92],"e":[94,185],"r":[96],"Subscript":[99,151,188],"m\">":[100,221],"<mml:semantics>":[101,154,190,222],"<mml:mrow>":[102,155,223],"<mml:msup>":[103,161,227],"<mml:mi>":[104],"\u2113":[105],"</mml:mi>":[106],"<mml:mrow":[107,117,159,192],"class=\"MJX-TeXAtom-ORD\">":[108,118,160,193],"<mml:mi>n</mml:mi>":[109,162,201,224],"<mml:mo>":[110],"\u2212":[111],"</mml:mo>":[112],"<mml:mi>m</mml:mi>":[113,128,228,233],"</mml:mrow>":[114,127,130,165,167,200,234],"</mml:msup>":[115,164,230],"<mml:msub>":[116,157,191],"<mml:mi":[119,121,123,125,194,196,198],"mathvariant=\"normal\">p</mml:mi>":[120],"mathvariant=\"normal\">e</mml:mi>":[122,197],"mathvariant=\"normal\">r</mml:mi>":[124],"mathvariant=\"normal\">m</mml:mi>":[126],"</mml:msub>":[129,166,202],"<mml:annotation":[131,168,203,235],"encoding=\"application/x-tex\">\\ell":[132],"^{n-m}\\mathrm":[133],"{perm}_m</mml:annotation>":[134],"</mml:semantics>":[135,170,206,237],"</mml:math>":[136,171,207,238],"</inline-formula>":[137,172,208,239],"be":[139],"realized":[140],"inside":[141],"alttext=\"upper":[147],"G":[148],"upper":[149],"L":[150],"squared\">":[153],"<mml:mi>G</mml:mi>":[156],"<mml:mi>L</mml:mi>":[158],"<mml:mn>2</mml:mn>":[163,226,229,232],"encoding=\"application/x-tex\">GL_{n^2}</mml:annotation>":[169],"-orbit":[173],"closure":[174],"determinant":[177,250],"alttext=\"normal":[182],"d":[183],"t":[187],"n\">":[189],"mathvariant=\"normal\">d</mml:mi>":[195],"mathvariant=\"normal\">t</mml:mi>":[199],"encoding=\"application/x-tex\">\\mathrm":[204],"{det}_n</mml:annotation>":[205],"when":[209],"alttext=\"n":[214],"greater-than":[215],"2":[216,220],"squared":[218],"plus":[219],"<mml:mo>&gt;</mml:mo>":[225],"<mml:mo>+</mml:mo>":[231],"encoding=\"application/x-tex\">n&gt;2m^2+2m</mml:annotation>":[236],".":[240],"Our":[241],"proof":[242],"relies":[243],"several":[245],"simple":[246],"degenerations":[247],"polynomial,":[251],"Macaulay\u2019s":[252],"theorem,":[253],"which":[254],"gives":[255],"growth":[261],"an":[263],"ideal,":[264],"estimate":[269],"from":[270],"regarding":[285],"determinant.":[292]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}