{"id":"https://openalex.org/W2164693112","doi":"https://doi.org/10.1090/s0025-5718-2010-02415-9","title":"Equivariant Gr\u00f6bner bases and the Gaussian two-factor model","display_name":"Equivariant Gr\u00f6bner bases and the Gaussian two-factor model","publication_year":2010,"publication_date":"2010-09-09","ids":{"openalex":"https://openalex.org/W2164693112","doi":"https://doi.org/10.1090/s0025-5718-2010-02415-9","mag":"2164693112"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2010-02415-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02415-9","pdf_url":"https://www.ams.org/mcom/2011-80-274/S0025-5718-2010-02415-9/S0025-5718-2010-02415-9.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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2011-80-274/S0025-5718-2010-02415-9/S0025-5718-2010-02415-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105369849","display_name":"Andries E. Brouwer","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Andries Brouwer","raw_affiliation_strings":["Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084270459","display_name":"Jan Draisma","orcid":"https://orcid.org/0000-0001-7248-8250"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]},{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Jan Draisma","raw_affiliation_strings":["Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands and Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands and Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I1341640284","https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.779,"has_fulltext":true,"cited_by_count":35,"citation_normalized_percentile":{"value":0.9345905,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"80","issue":"274","first_page":"1123","last_page":"1133"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9865000247955322,"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/T11752","display_name":"Cancer Treatment and Pharmacology","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8624260425567627},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.8194378614425659},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.6416524052619934},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.6380345821380615},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6079320907592773},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5515251159667969},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.5255920886993408},{"id":"https://openalex.org/keywords/general-linear-group","display_name":"General linear group","score":0.5037562251091003},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.5031363368034363},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.4784645736217499},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.47277238965034485},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3798644244670868},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33745381236076355},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.28975939750671387}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8624260425567627},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.8194378614425659},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.6416524052619934},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.6380345821380615},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6079320907592773},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5515251159667969},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5255920886993408},{"id":"https://openalex.org/C172331165","wikidata":"https://www.wikidata.org/wiki/Q524607","display_name":"General linear group","level":3,"score":0.5037562251091003},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.5031363368034363},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.4784645736217499},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.47277238965034485},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3798644244670868},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33745381236076355},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.28975939750671387},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":12,"locations":[{"id":"doi:10.1090/s0025-5718-2010-02415-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02415-9","pdf_url":"https://www.ams.org/mcom/2011-80-274/S0025-5718-2010-02415-9/S0025-5718-2010-02415-9.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:pure.tue.nl:openaire_cris_publications/2601b0b8-1025-4b33-aaba-9eb0646d4fea","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/2601b0b8-1025-4b33-aaba-9eb0646d4fea","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Brouwer, A E & Draisma, J 2011, 'Equivariant Gr\u00f6bner bases and the Gaussian two-factor model', Mathematics of Computation, vol. 80, no. 274, pp. 1123-1133. https://doi.org/10.1090/S0025-5718-2010-02415-9","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.tue.nl:publications/c49c2ab0-9418-438c-b60a-4f8bd366c8f9","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/c49c2ab0-9418-438c-b60a-4f8bd366c8f9","pdf_url":"http://arxiv.org/pdf/0908.1530","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":"Brouwer, A E & Draisma, J 2009, Equivariant Gr\u00f6bner bases and the Gaussian two-factor model. arXiv.org [math.AC], vol. 0908.1530, s.n.","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:685962","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=685962","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","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":"ISSN:0025-5718","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.249.4301","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.249.4301","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0908.1530v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.249.5081","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.249.5081","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0908.1530v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.420.9143","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.420.9143","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.win.tue.nl/~aeb/preprints/ggb6.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.421.2888","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.421.2888","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.win.tue.nl/~aeb/preprints/ggb10a.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.747.1482","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.747.1482","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0908.1530.pdf","raw_type":"text"},{"id":"pmh:oai:library.tue.nl:685962","is_oa":false,"landing_page_url":"http://repository.tue.nl/685962","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","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":"ISSN:0025-5718","raw_type":"Article / Letter to the editor"},{"id":"pmh:tue:oai:library.tue.nl:894308","is_oa":false,"landing_page_url":"http://repository.tue.nl/894308","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:tue:oai:pure.tue.nl:publications/2601b0b8-1025-4b33-aaba-9eb0646d4fea","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/2601b0b8-1025-4b33-aaba-9eb0646d4fea","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 80(274), 1123 - 1133. American Mathematical Society","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2010-02415-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02415-9","pdf_url":"https://www.ams.org/mcom/2011-80-274/S0025-5718-2010-02415-9/S0025-5718-2010-02415-9.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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2164693112.pdf","grobid_xml":"https://content.openalex.org/works/W2164693112.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1592163810","https://openalex.org/W1967341303","https://openalex.org/W1973722201","https://openalex.org/W1984588726","https://openalex.org/W2040464112","https://openalex.org/W2044502250","https://openalex.org/W2045555514","https://openalex.org/W2061059337","https://openalex.org/W2062617333","https://openalex.org/W2076213737","https://openalex.org/W2109011623","https://openalex.org/W2962887899","https://openalex.org/W2963495298","https://openalex.org/W2963673163","https://openalex.org/W2963985952","https://openalex.org/W3122804471"],"related_works":["https://openalex.org/W2891471055","https://openalex.org/W1496720970","https://openalex.org/W2963854314","https://openalex.org/W4291612424","https://openalex.org/W2090726416","https://openalex.org/W1985218657","https://openalex.org/W4226371494","https://openalex.org/W2157756491","https://openalex.org/W2164693112","https://openalex.org/W2953033677"],"abstract_inverted_index":{"Exploiting":[0],"symmetry":[1,10],"in":[2,22,61,72],"Gr\u00f6bner":[3,59,100],"basis":[4],"computations":[5],"is":[6,27,364],"difficult":[7],"when":[8],"the":[9,12,31,34,55,80,106,152,155,410],"takes":[11],"form":[13],"of":[14,49,57,108,154,369],"a":[15,41,62,65,85,94,402],"group":[16,35],"acting":[17],"by":[18,47,68,366,404],"automorphisms":[19],"on":[20,70,409],"monomials":[21,71],"finitely":[23],"many":[24,75],"variables.":[25,76],"This":[26,400],"largely":[28],"due":[29],"to":[30],"fact":[32],"that":[33,79,151],"elements,":[36],"being":[37],"invertible,":[38],"cannot":[39],"preserve":[40],"term":[42,86],"order.":[43],"By":[44],"contrast,":[45],"inspired":[46],"work":[48],"Aschenbrenner":[50],"and":[51,88,105,397,407],"Hillar,":[52],"we":[53,149],"introduce":[54],"concept":[56],"<italic>equivariant":[58],"basis</italic>":[60],"setting":[63],"where":[64],"<italic>monoid</italic>":[66],"acts":[67],"<italic>homomorphisms</italic>":[69],"potentially":[73],"<italic>infinitely</italic>":[74],"We":[77],"require":[78],"action":[81],"be":[82],"compatible":[83],"with":[84],"order,":[87],"under":[89],"some":[90],"further":[91],"assumptions":[92],"derive":[93],"Buchberger-type":[95],"algorithm":[96,104],"for":[97],"computing":[98],"equivariant":[99],"bases.":[101],"Using":[102],"this":[103],"monoid":[107],"strictly":[109],"increasing":[110],"functions":[111],"<inline-formula":[112,373],"content-type=\"math/mathml\">":[113,159,374],"<mml:math":[114,161,375],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[115,162,376],"alttext=\"double-struck":[116,163],"upper":[117,121,164,178,187,203],"N":[118,179,204],"right-arrow":[119,185,212],"double-struck":[120,177,186,202],"N\">":[122],"<mml:semantics>":[123,232,380],"<mml:mrow>":[124,233,381],"<mml:mrow":[125,134,234,243,258,273,296,308],"class=\"MJX-TeXAtom-ORD\">":[126,135,235,244,259,274,297,309],"<mml:mi":[127,136,236,260,275,298],"mathvariant=\"double-struck\">N</mml:mi>":[128,137,261,299],"</mml:mrow>":[129,138,139,238,247,262,277,300,312,335,387],"<mml:mo":[130,239,267,269,278,301,314],"stretchy=\"false\">":[131,270,315],"\u2192":[132,271],"</mml:mo>":[133,251,257,272,291,295,317,385],"<mml:annotation":[140,336,388],"encoding=\"application/x-tex\">\\mathbb":[141,337],"{N}":[142],"\\to":[143,347],"\\mathbb":[144,342,348,353],"{N}</mml:annotation>":[145],"</mml:semantics>":[146,360,392],"</mml:math>":[147,361,393],"</inline-formula>":[148,394],"prove":[150],"kernel":[153],"ring":[156],"homomorphism":[157],"<disp-formula":[158],"\\[":[160],"R":[165,188],"left-bracket":[166,189],"y":[167,207],"Subscript":[168,191,196,208,216,220,225,229],"i":[169,173,181,192,197,200,209,217,226,344,351],"j":[170,175,183,210,221,230],"Baseline":[171,193,198,211,218,222,227],"bar":[172,199,214],"comma":[174,180,194,206],"element-of":[176,201],"greater-than":[182],"right-bracket":[184,205],"s":[190,215,219],"t":[195,224,228],"from":[213,414],"plus":[223],"Baseline\">":[231],"mathvariant=\"double-struck\">R</mml:mi>":[237,276],"stretchy=\"false\">[</mml:mo>":[240,279],"<mml:msub>":[241,280,285,306,318,322,327,331],"<mml:mi>y</mml:mi>":[242,307],"<mml:mi>i</mml:mi>":[245,252,264,282,287,292,310,320,329],"<mml:mi>j</mml:mi>":[246,254,266,311,324,333],"</mml:msub>":[248,283,288,313,321,325,330,334],"<mml:mo>":[249,255,289,293,383],"\u2223":[250,290],"<mml:mo>,</mml:mo>":[253,263,284,303],"\u2208":[256,294],"<mml:mo>&gt;</mml:mo>":[265],"stretchy=\"false\">]</mml:mo>":[268,302],"<mml:mi>s</mml:mi>":[281,319,323],"<mml:mi>t</mml:mi>":[286,328,332],"<mml:mtext>":[304],"</mml:mtext>":[305],"\u21a6":[316],"<mml:mo>+</mml:mo>":[326],"{R}[y_{ij}":[338],"\\mid":[339,350],"i,j":[340],"\\in":[341,352],"{N},":[343],"&gt;":[345],"j]":[346],"{R}[s_i,t_i":[349],"{N}],\\":[354],"y_{ij}":[355],"\\mapsto":[356],"s_is_j":[357],"+":[358],"t_it_j</mml:annotation>":[359],"\\]":[362],"</disp-formula>":[363],"generated":[365],"two":[367],"types":[368],"polynomials:":[370],"<italic>":[371],"off-diagonal":[372],"alttext=\"3":[377],"times":[378],"3\">":[379],"<mml:mn>3</mml:mn>":[382,386],"\u00d7":[384],"encoding=\"application/x-tex\">3":[389],"\\times":[390],"3</mml:annotation>":[391],"-minors":[395],"</italic>":[396],"<italic>pentads</italic>":[398],".":[399],"confirms":[401],"conjecture":[403],"Drton,":[405],"Sturmfels,":[406],"Sullivant":[408],"Gaussian":[411],"two-factor":[412],"model":[413],"algebraic":[415],"statistics.":[416]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
