{"id":"https://openalex.org/W2045252454","doi":"https://doi.org/10.1145/1577190.1577204","title":"A proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions","display_name":"A proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions","publication_year":2009,"publication_date":"2009-08-03","ids":{"openalex":"https://openalex.org/W2045252454","doi":"https://doi.org/10.1145/1577190.1577204","mag":"2045252454"},"language":"en","primary_location":{"id":"doi:10.1145/1577190.1577204","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1577190.1577204","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 conference on Symbolic numeric computation","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/A5056874049","display_name":"Erich Kaltofen","orcid":"https://orcid.org/0000-0003-2739-3230"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Erich Kaltofen","raw_affiliation_strings":["North Carolina State University, Raleigh, NC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"North Carolina State University, Raleigh, NC, USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050832305","display_name":"Zhengfeng Yang","orcid":"https://orcid.org/0000-0003-2011-9466"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengfeng Yang","raw_affiliation_strings":["East China Normal University, Shanghai, China","East China Normal University, SHANGHAI, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I66867065"]},{"raw_affiliation_string":"East China Normal University, SHANGHAI, China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026679766","display_name":"Lihong Zhi","orcid":"https://orcid.org/0000-0001-9973-2217"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lihong Zhi","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Beijing, China","institution_ids":["https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3865,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.87226277,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"65","last_page":"70"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8294370770454407},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7940043210983276},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7677112817764282},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6803605556488037},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5790138840675354},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5389547944068909},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4936767518520355},{"id":"https://openalex.org/keywords/column","display_name":"Column (typography)","score":0.4914323091506958},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.4898640811443329},{"id":"https://openalex.org/keywords/hurwitz-matrix","display_name":"Hurwitz matrix","score":0.42903172969818115},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.424307644367218},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41204074025154114},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3202088177204132},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.17252632975578308},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15884855389595032},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08029162883758545}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8294370770454407},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7940043210983276},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7677112817764282},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6803605556488037},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5790138840675354},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5389547944068909},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4936767518520355},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.4914323091506958},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.4898640811443329},{"id":"https://openalex.org/C198931094","wikidata":"https://www.wikidata.org/wiki/Q2610096","display_name":"Hurwitz matrix","level":3,"score":0.42903172969818115},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.424307644367218},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41204074025154114},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3202088177204132},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.17252632975578308},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15884855389595032},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08029162883758545},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1577190.1577204","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1577190.1577204","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 conference on Symbolic numeric computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.149.7752","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.7752","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www4.ncsu.edu/~kaltofen/bibliography/09/KYZ09.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W119962296","https://openalex.org/W1967073510","https://openalex.org/W1982216340","https://openalex.org/W2001033871","https://openalex.org/W2002341633","https://openalex.org/W2016389104","https://openalex.org/W2058134063","https://openalex.org/W2065276731","https://openalex.org/W2067436377","https://openalex.org/W2536620281"],"related_works":["https://openalex.org/W4301895170","https://openalex.org/W2181722423","https://openalex.org/W2163760347","https://openalex.org/W2963936214","https://openalex.org/W2610026222","https://openalex.org/W2347222412","https://openalex.org/W2085601491","https://openalex.org/W4233024372","https://openalex.org/W2263870431","https://openalex.org/W1936734204"],"abstract_inverted_index":{"For":[0],"a":[1,56],"proof":[2],"of":[3,26,35,44,47,72],"the":[4,24,36,39,42,45],"monotone":[5],"column":[6],"permanent":[7],"(MCP)":[8],"conjecture":[9],"for":[10,31,60],"dimension":[11],"4":[12,19],"it":[13],"is":[14],"sufficient":[15],"to":[16],"show":[17],"that":[18,62],"polynomials,":[20],"which":[21],"come":[22],"from":[23],"permanents":[25],"real":[27,33],"matrices,":[28],"are":[29,50],"nonnegative":[30],"all":[32,51],"values":[34],"variables,":[37],"where":[38],"degrees":[40],"and":[41],"number":[43],"variables":[46],"these":[48,63],"polynomials":[49,64],"8.":[52],"Here":[53],"we":[54],"apply":[55],"hybrid":[57],"symbolic-numerical":[58],"algorithm":[59],"certifying":[61],"can":[65],"be":[66],"written":[67],"as":[68],"an":[69],"exact":[70],"fraction":[71],"two":[73],"polynomial":[74],"sums-of-squares":[75],"(SOS)":[76],"with":[77],"rational":[78],"coefficients.":[79]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}