{"id":"https://openalex.org/W2797915221","doi":"https://doi.org/10.1137/18m1181912","title":"A Polyhedral Method for Sparse Systems with Many Positive Solutions","display_name":"A Polyhedral Method for Sparse Systems with Many Positive Solutions","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2797915221","doi":"https://doi.org/10.1137/18m1181912","mag":"2797915221"},"language":"en","primary_location":{"id":"doi:10.1137/18m1181912","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1181912","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1181912","source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1181912","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Fr\u00e9d\u00e9ric Bihan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fr\u00e9d\u00e9ric Bihan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Francisco Santos","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Francisco Santos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Pierre-Jean Spaenlehauer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pierre-Jean Spaenlehauer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2895,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.81957428,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2","issue":"4","first_page":"620","last_page":"645"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.840399980545044,"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":0.840399980545044,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.10000000149011612,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.030500000342726707,"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/polytope","display_name":"Polytope","score":0.8050000071525574},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.7383999824523926},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5586000084877014},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5430999994277954},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5346999764442444},{"id":"https://openalex.org/keywords/mixed-volume","display_name":"Mixed volume","score":0.44999998807907104}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8050000071525574},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7437000274658203},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.7383999824523926},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5586000084877014},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5430999994277954},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5346999764442444},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5292999744415283},{"id":"https://openalex.org/C44550424","wikidata":"https://www.wikidata.org/wiki/Q4424496","display_name":"Mixed volume","level":5,"score":0.44999998807907104},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41690000891685486},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.38100001215934753},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.3727000057697296},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.2639999985694885}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/18m1181912","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1181912","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1181912","source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"},{"id":"pmh:oai:repositorio.unican.es:10902/34559","is_oa":false,"landing_page_url":"https://hdl.handle.net/10902/34559","pdf_url":null,"source":{"id":"https://openalex.org/S4306400398","display_name":"UCrea (University of Cantabria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13134134","host_organization_name":"Universidad de Cantabria","host_organization_lineage":["https://openalex.org/I13134134"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry, 2018, 2(4), 620-645","raw_type":"publishedVersion"},{"id":"pmh:oai:arXiv.org:1804.05683","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.05683","pdf_url":"https://arxiv.org/pdf/1804.05683","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":"pmh:oai:HAL:hal-01877602v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-01877602","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry, 2018, 2 (4), pp.620-645. ⟨10.1137/18M1181912⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-04723393v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04723393","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry, 2018, 2 (4), pp.620-645. ⟨10.1137/18M1181912⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1137/18m1181912","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1181912","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1181912","source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G202495085","display_name":null,"funder_award_id":"1440140","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G4402292705","display_name":null,"funder_award_id":"DMS-1440140","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5969482202","display_name":null,"funder_award_id":"DMS-1440140","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G7403938415","display_name":null,"funder_award_id":"DMS-1440140","funder_id":"https://openalex.org/F4320323688","funder_display_name":"Einstein Stiftung Berlin"},{"id":"https://openalex.org/G811546825","display_name":null,"funder_award_id":"1440140","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"},{"id":"https://openalex.org/F4320323688","display_name":"Einstein Stiftung Berlin","ror":"https://ror.org/03s0fv852"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2797915221.pdf","grobid_xml":"https://content.openalex.org/works/W2797915221.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1611937190","https://openalex.org/W1827575274","https://openalex.org/W2023858111","https://openalex.org/W2045191540","https://openalex.org/W2074835688","https://openalex.org/W2143023483","https://openalex.org/W2163614899","https://openalex.org/W2607033560","https://openalex.org/W2963391858","https://openalex.org/W2964235411","https://openalex.org/W4236154823"],"related_works":[],"abstract_inverted_index":{"We":[0,119],"investigate":[1],"a":[2,53,64,87,129],"version":[3],"of":[4,19,23,28,40,46,66,79,83,95,106,109,115,124],"Viro's":[5],"method":[6,34],"for":[7,102],"constructing":[8],"polynomial":[9,110],"systems":[10,111],"with":[11,32,112],"many":[12],"positive":[13,29,50,107],"solutions,":[14],"based":[15],"on":[16],"regular":[17,68],"triangulations":[18],"the":[20,24,38,41,47,80,98,103,122],"Newton":[21],"polytope":[22],"system.":[25],"The":[26],"number":[27,105],"solutions":[30,108],"obtained":[31],"our":[33],"is":[35,52,60],"governed":[36],"by":[37],"size":[39],"largest":[42],"positively":[43,76],"decorable":[44,77],"subcomplex":[45,65],"triangulation.":[48,69],"Here,":[49],"decorability":[51],"property":[54],"that":[55],"we":[56,73,89],"introduce":[57],"and":[58,117,127],"which":[59],"dual":[61],"to":[62],"being":[63,97],"some":[67,94],"Using":[70],"this":[71],"duality,":[72],"produce":[74],"large":[75],"subcomplexes":[78],"boundary":[81],"complexes":[82],"cyclic":[84],"polytopes.":[85],"As":[86],"byproduct,":[88],"get":[90],"new":[91],"lower":[92],"bounds,":[93],"them":[96],"best":[99],"currently":[100],"known,":[101],"maximal":[104],"prescribed":[113],"numbers":[114,126],"monomials":[116],"variables.":[118],"also":[120],"study":[121],"asymptotics":[123],"these":[125],"observe":[128],"log-concavity":[130],"property.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2018-04-24T00:00:00"}