{"id":"https://openalex.org/W2003979730","doi":"https://doi.org/10.1145/1132516.1132578","title":"Hyperbolic polynomials approach to Van der Waerden/Schrijver-Valiant like conjectures","display_name":"Hyperbolic polynomials approach to Van der Waerden/Schrijver-Valiant like conjectures","publication_year":2006,"publication_date":"2006-05-21","ids":{"openalex":"https://openalex.org/W2003979730","doi":"https://doi.org/10.1145/1132516.1132578","mag":"2003979730"},"language":"en","primary_location":{"id":"doi:10.1145/1132516.1132578","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1132516.1132578","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","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/A5022317936","display_name":"Leonid Gurvits","orcid":"https://orcid.org/0000-0002-0694-2459"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Leonid Gurvits","raw_affiliation_strings":["Los Alamos National Laboratory, Los Alamos, NM"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Los Alamos National Laboratory, Los Alamos, NM","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022317936"],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":null,"apc_paid":null,"fwci":7.3597,"has_fulltext":false,"cited_by_count":69,"citation_normalized_percentile":{"value":0.98297594,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"417","last_page":"426"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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":0.996999979019165,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9965000152587891,"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/van-der-waerdens-theorem","display_name":"Van der Waerden's theorem","score":0.8746010661125183},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7963542938232422},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7461167573928833},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.7238684892654419},{"id":"https://openalex.org/keywords/orthant","display_name":"Orthant","score":0.6604558229446411},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6512686610221863},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5736343264579773},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48574763536453247},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.4731220602989197},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.42145463824272156},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4137084484100342},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3254464268684387},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17693838477134705},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.15542542934417725},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13499045372009277}],"concepts":[{"id":"https://openalex.org/C116493835","wikidata":"https://www.wikidata.org/wiki/Q764287","display_name":"Van der Waerden's theorem","level":2,"score":0.8746010661125183},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7963542938232422},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7461167573928833},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.7238684892654419},{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.6604558229446411},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6512686610221863},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5736343264579773},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48574763536453247},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.4731220602989197},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.42145463824272156},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4137084484100342},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3254464268684387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17693838477134705},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.15542542934417725},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13499045372009277},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1132516.1132578","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1132516.1132578","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1532154335","https://openalex.org/W1535255862","https://openalex.org/W1571966798","https://openalex.org/W1595424428","https://openalex.org/W1626791968","https://openalex.org/W1632601927","https://openalex.org/W1967139274","https://openalex.org/W1985376214","https://openalex.org/W1997454240","https://openalex.org/W1999344551","https://openalex.org/W2016724581","https://openalex.org/W2022242474","https://openalex.org/W2022807319","https://openalex.org/W2025202934","https://openalex.org/W2027584441","https://openalex.org/W2052125266","https://openalex.org/W2066894529","https://openalex.org/W2081357884","https://openalex.org/W2100440346","https://openalex.org/W2100552771","https://openalex.org/W2116488705","https://openalex.org/W2140211422","https://openalex.org/W2152309892","https://openalex.org/W2153400929","https://openalex.org/W2162471115","https://openalex.org/W2162960148","https://openalex.org/W2169767216","https://openalex.org/W2196559987","https://openalex.org/W2317283549","https://openalex.org/W2517666786","https://openalex.org/W2610680804","https://openalex.org/W2798707604","https://openalex.org/W2950165770","https://openalex.org/W2952104194","https://openalex.org/W2952940702","https://openalex.org/W3106367349","https://openalex.org/W3123082523","https://openalex.org/W3187249085","https://openalex.org/W6699171882"],"related_works":["https://openalex.org/W2077043254","https://openalex.org/W1993502443","https://openalex.org/W4285792756","https://openalex.org/W2003979730","https://openalex.org/W2952104194","https://openalex.org/W2014479920","https://openalex.org/W359048411","https://openalex.org/W1982433837","https://openalex.org/W1599657576","https://openalex.org/W2963345594"],"abstract_inverted_index":{"Let":[0],"p(x1,...,xn)":[1],"=":[2,20,53,139,177],"p(X)":[3],",":[4,179,336],"X":[5,43,88],"\u2208":[6,22,44,89],"Rn":[7,23,45],"be":[8,24],"a":[9,25,32,130,185,275,291,301,325,331],"homogeneous":[10],"polynomial":[11,33,48,79,133,276],"of":[12,27,66,86,122,134,190,199,212,231,262,271,283,308],"degree":[13,135],"n":[14,16,148,173,284,286,309,311],"in":[15,117,215,320],"real":[17,41,57],"variables,":[18],"e":[19],"(1,1,..,1)":[21],"vector":[26],"all":[28,40,56],"ones":[29],".":[30,181],"Such":[31],"p":[34,80],"is":[35,74,81,129,184,238],"called":[36,75,82],"e-hyperbolic":[37,78],"if":[38,84,127],"for":[39,112,295],"vectors":[42,87],"the":[46,102,113,160,191,197,206,210,225,272,281,306],"univariate":[47],"equation":[49],"p(te":[50],"-":[51],"X)":[52],"0":[54,72],"has":[55],"roots":[58,68,85],"\u03bb1(X)":[59],"\u2265":[60,62,143,168],"...":[61],"\u03bbn(X).":[63],"The":[64,119],"number":[65,211],"nonzero":[67,318],"|i":[69],":\u03bbi(X)":[70],"\u2260":[71],"|":[73],"Rankp(X).":[76],"An":[77],"POS-hyperbolic":[83,131,226],"Rn+":[90,99],"with":[91,234],"nonnegative":[92,96,235],"coordinates":[93],"are":[94,229],"also":[95],"(the":[97],"orthant":[98],"belongs":[100],"to":[101,224,323,340,352],"hyperbolic":[103,263],"cone)":[104],"and":[105,141,241,250,300,342,345,357],"p(e)":[106],">":[107,152],"0.":[108],"Below":[109],"e1,...,en":[110],"stands":[111],"canonical":[114],"orthogonal":[115],"basis":[116],"Rn.":[118],"main":[120],"results":[121,222,348],"this":[123],"paper":[124,329],"states":[125],"that":[126],"p(x1,x2,...,xn)":[128,142],"(homogeneous)":[132],"n,":[136,158],"Rankp":[137],"(ei)":[138],"Ri":[140],"\u220f1":[144,169],"\u2264":[145,147,155,157,170,172],"i":[146,156,171],"xi":[149,151],";":[150],"0,":[153],"1":[154],"then":[159],"following":[161],"inequality":[162,183],"holds":[163],"\u2202n/\u2202":[164],"x1...\u2202":[165],"xn":[166],"p(0,...,0)":[167],"(Gi-1/Gi)Gi-1,":[174],"where":[175],"Gi":[176],"min(Ri":[178],"n+1-i)":[180],"This":[182],"vast":[186],"(and":[187],"unifying)":[188],"generalization":[189],"van":[192],"der":[193],"Waerden":[194],"conjecture":[195,208],"on":[196,209],"permanents":[198],"doubly":[200],"stochastic":[201],"matrices":[202,289],"as":[203,205,349,351],"well":[204,350],"Schrijver-Valiant":[207],"perfect":[213],"matchings":[214],"k-regular":[216],"bipartite":[217],"graphs.":[218],"These":[219],"two":[220],"famous":[221],"correspond":[223],"polynomials":[227],"which":[228,337],"products":[230],"linear":[232],"forms":[233],"coefficients.Our":[236],"proof":[237],"relatively":[239],"simple":[240],"\"noncomputational\";":[242],"it":[243],"actually":[244],"slightly":[245],"improves":[246],"Schrijver's":[247],"lower":[248],"bound,":[249],"uses":[251],"very":[252],"basic":[253],"(more":[254],"or":[255],"less":[256],"centered":[257],"around":[258],"Rolle's":[259],"theorem)":[260],"properties":[261],"polynomials.":[264],"We":[265],"present":[266],"some":[267],"important":[268,355],"algorithmic":[269],"applications":[270],"result,":[273],"including":[274],"time":[277],"deterministic":[278,302],"algorithm":[279,304],"approximating":[280,305],"permanent":[282,307],"x":[285,310],"entry-wise":[287],"non-negative":[288],"within":[290,324],"multiplicative":[292,326],"factor":[293,327],"en/nm":[294],"any":[296],"fixed":[297],"positive":[298],"m;":[299],"poly-time":[303],"matrix":[312],"A":[313],"having":[314],"at":[315],"most":[316],"k":[317],"entries":[319],"each":[321],"column":[322],"(k-1/k)(k-1)n.This":[328],"introduces":[330],"new":[332,354,359],"powerful":[333],"\"polynomial\"":[334],"technique":[335],"allows":[338],"us":[339],"simplify":[341],"unify":[343],"hard":[344],"key":[346],"known":[347],"prove":[353],"theorems":[356],"get":[358],"algorithms.":[360]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}