{"id":"https://openalex.org/W7220729938","doi":"https://doi.org/10.48550/arxiv.2610.06435","title":"Descartes' rule of signs for arbitrary fewnomial systems","display_name":"Descartes' rule of signs for arbitrary fewnomial systems","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220729938","doi":"https://doi.org/10.48550/arxiv.2610.06435"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.06435","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06435","pdf_url":"https://arxiv.org/pdf/2610.06435","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.06435","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024769926","display_name":"Fr\u00e9d\u00e9ric Bihan","orcid":"https://orcid.org/0000-0002-9754-3815","observed_orcids":["https://orcid.org/0000-0002-9754-3815"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bihan, Fr\u00e9d\u00e9ric","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5024769926"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9526000022888184,"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":0.9526000022888184,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.02800000086426735,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.014600000344216824,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/descartes-rule-of-signs","display_name":"Descartes' rule of signs","score":0.9959999918937683},{"id":"https://openalex.org/keywords/multivariate-polynomial-systems","display_name":"multivariate polynomial systems","score":0.6930000185966492},{"id":"https://openalex.org/keywords/oriented-matroids","display_name":"oriented matroids","score":0.9440000057220459},{"id":"https://openalex.org/keywords/maximal-minors","display_name":"maximal minors","score":0.6119999885559082},{"id":"https://openalex.org/keywords/hyperplane-arrangements","display_name":"hyperplane arrangements","score":0.8059999942779541},{"id":"https://openalex.org/keywords/topological-degree","display_name":"topological degree","score":0.7820000052452087},{"id":"https://openalex.org/keywords/circuits","display_name":"circuits","score":0.546999990940094},{"id":"https://openalex.org/keywords/sign-conditions","display_name":"sign conditions","score":0.3790000081062317}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8565000295639038},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5432000160217285},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.5231000185012817},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4957999885082245},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.48089998960494995},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4796000123023987},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.47940000891685486},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.47780001163482666},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4771000146865845},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4537999927997589},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4309999942779541},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4097000062465668},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.3790999948978424},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.3781999945640564},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.35089999437332153},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32679998874664307},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.3190999925136566},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.28439998626708984},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.2662999927997589},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2535000145435333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.06435","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06435","pdf_url":"https://arxiv.org/pdf/2610.06435","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.06435","doi":"https://doi.org/10.48550/arxiv.2610.06435","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.06435","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.06435","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06435","pdf_url":"https://arxiv.org/pdf/2610.06435","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220729938.pdf","grobid_xml":"https://content.openalex.org/works/W7220729938.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2021877860","https://openalex.org/W2164133693","https://openalex.org/W2607033560"],"related_works":["https://openalex.org/W2255150232","https://openalex.org/W3169600249","https://openalex.org/W3092965019","https://openalex.org/W3187068134","https://openalex.org/W2234351191","https://openalex.org/W2598984576","https://openalex.org/W6999661890","https://openalex.org/W2608273459","https://openalex.org/W2749702101","https://openalex.org/W7098277310"],"abstract_inverted_index":{"The":[0],"classical":[1],"Descartes'":[2],"rule":[3,64],"of":[4,9,12,22,25,35,42,51,62,71,89,103,108,122,126,141,153,165,177,185,214,216,221,233,257],"signs":[5,41,123,213],"bounds":[6,85,253],"the":[7,20,33,36,40,43,48,52,87,100,104,109,119,134,138,147,174,178,183,189,193,197,212,222,231,234,241,249,252,255,258,261],"number":[8,21,88,184,191],"positive":[10,91],"roots":[11],"a":[13,59,157,163,166,201,208,217,228],"real":[14,73],"polynomial":[15,74],"in":[16,76,156,196],"one":[17],"variable":[18],"by":[19,173,188,200,207],"sign":[23,97,264],"changes":[24],"its":[26,113],"coefficients.":[27],"This":[28,160,225],"bound":[29,182],"only":[30,94],"depends":[31],"on":[32,39,47,96,99,238,266],"order":[34],"exponents":[37,262],"and":[38,54,107,112,128,137,143,260],"coefficients,":[44],"that":[45],"is,":[46],"oriented":[49,175],"matroids":[50],"exponent":[53,110,223],"coefficient":[55,105,179],"matrices.":[56],"We":[57,181],"give":[58],"multivariate":[60],"generalization":[61],"this":[63,247],"to":[65,149,227],"arbitrary":[66],"fewnomial":[67],"systems:":[68],"for":[69,86,124,244],"systems":[70],"$n$":[72,77],"equations":[75],"variables":[78],"with":[79,240],"$n+k+1$":[80],"monomials,":[81],"we":[82,205],"obtain":[83],"upper":[84],"nondegenerate":[90],"solutions":[92],"which":[93,145,204,236],"depend":[95],"conditions":[98,265],"maximal":[101],"minors":[102,215],"matrix":[106,111,220],"liftings.":[114],"For":[115],"$k=1$":[116],"they":[117],"are":[118],"Descartes":[120,242],"rules":[121,243],"circuits":[125],"Bihan-Dickenstein":[127],"Bihan-Dickenstein-Forsg\u00e5rd.":[129],"Our":[130],"approach":[131],"starts":[132],"from":[133],"Gale":[135,218],"duality":[136],"Khovanskii-Rolle":[139],"argument":[140],"Bihan":[142],"Sottile,":[144],"reduce":[146],"problem":[148],"counting":[150],"common":[151],"zeros":[152,187,194],"iterated":[154],"Jacobians":[155],"polyhedron":[158,161],"$\u0394$.":[159],"is":[162,171],"chamber":[164],"hyperplane":[167],"arrangement":[168],"whose":[169],"combinatorics":[170,256],"determined":[172],"matroid":[176],"matrix.":[180,224],"these":[186],"B\u00e9zout":[190],"minus":[192],"forced":[195],"other":[198],"chambers":[199],"topological":[202],"degree,":[203],"compute":[206],"facet-count":[209],"formula":[210],"involving":[211],"dual":[219],"leads":[226],"recursion":[229],"over":[230],"flats":[232],"arrangement,":[235,259],"ends":[237],"lines":[239],"circuits.":[245],"In":[246],"way":[248],"coefficients":[250],"enter":[251],"through":[254,263],"minors.":[267]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-07T00:00:00"}