{"id":"https://openalex.org/W2038079294","doi":"https://doi.org/10.1145/1390768.1390797","title":"Hilbert's nullstellensatz and an algorithm for proving combinatorial infeasibility","display_name":"Hilbert's nullstellensatz and an algorithm for proving combinatorial infeasibility","publication_year":2008,"publication_date":"2008-07-20","ids":{"openalex":"https://openalex.org/W2038079294","doi":"https://doi.org/10.1145/1390768.1390797","mag":"2038079294"},"language":"en","primary_location":{"id":"doi:10.1145/1390768.1390797","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1390768.1390797","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-first international symposium on Symbolic and algebraic 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/A5055755657","display_name":"Jes\u00fas A. De Loera","orcid":"https://orcid.org/0000-0002-9556-1112"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. A. De Loera","raw_affiliation_strings":["Univ. of California at Davis, Davis, CA, USA","University of California at Davis, Davis, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of California at Davis, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"University of California at Davis, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031373908","display_name":"Jon Lee","orcid":"https://orcid.org/0000-0002-8190-1091"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Lee","raw_affiliation_strings":["IBM T.J. Watson Research Center, Yorktown Heights, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM T.J. Watson Research Center, Yorktown Heights, CA, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086599845","display_name":"Peter N. Malkin","orcid":null},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. N. Malkin","raw_affiliation_strings":["Univ. of California at Davis, Davis, CA, USA","University of California at Davis, Davis, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of California at Davis, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"University of California at Davis, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005906505","display_name":"Susan S. Margulies","orcid":"https://orcid.org/0000-0002-3615-7902"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Margulies","raw_affiliation_strings":["Univ. of California at Davis, Davis, CA, USA","University of California at Davis, Davis, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of California at Davis, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"University of California at Davis, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3117,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.91740244,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"197","last_page":"206"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9979000091552734,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9864000082015991,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/system-of-polynomial-equations","display_name":"System of polynomial equations","score":0.5718350410461426},{"id":"https://openalex.org/keywords/combinatorial-algorithms","display_name":"Combinatorial algorithms","score":0.5442647337913513},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.541610598564148},{"id":"https://openalex.org/keywords/combinatorial-principles","display_name":"Combinatorial principles","score":0.4806877076625824},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47648924589157104},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"Combinatorial optimization","score":0.4747472405433655},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4361186921596527},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.427154004573822},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3967413306236267},{"id":"https://openalex.org/keywords/combinatorial-explosion","display_name":"Combinatorial explosion","score":0.3830412030220032},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3828176259994507}],"concepts":[{"id":"https://openalex.org/C105335568","wikidata":"https://www.wikidata.org/wiki/Q7663735","display_name":"System of polynomial equations","level":3,"score":0.5718350410461426},{"id":"https://openalex.org/C2988809283","wikidata":"https://www.wikidata.org/wiki/Q1514868","display_name":"Combinatorial algorithms","level":2,"score":0.5442647337913513},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.541610598564148},{"id":"https://openalex.org/C1769372","wikidata":"https://www.wikidata.org/wiki/Q3850844","display_name":"Combinatorial principles","level":3,"score":0.4806877076625824},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47648924589157104},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.4747472405433655},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4361186921596527},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.427154004573822},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3967413306236267},{"id":"https://openalex.org/C115908005","wikidata":"https://www.wikidata.org/wiki/Q2668364","display_name":"Combinatorial explosion","level":2,"score":0.3830412030220032},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3828176259994507},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1145/1390768.1390797","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1390768.1390797","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-first international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.156.5544","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.5544","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucdavis.edu/~deloera/RECENT_WORK/nulla_issac_10.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.395.7481","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.395.7481","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cecm.sfu.ca/personal/monaganm/teaching/MATH439/margulies.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.93.7846","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.93.7846","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucdavis.edu/~deloera/MISC/ADMIN/nulla_issac.pdf","raw_type":"text"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt9g5835pj","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/9g5835pj","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:qt9g5835pj","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/9g5835pj","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"De Loera, J. A.; Lee, J.; Malkin, P.; &amp; Margulies, S.(2008). Hilbert's Nullstellensatz and an Algorithm for Proving Combinatorial\\n         Infeasibility. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/9g5835pj","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W64656188","https://openalex.org/W134868435","https://openalex.org/W194598513","https://openalex.org/W1505369303","https://openalex.org/W1698110770","https://openalex.org/W1967184028","https://openalex.org/W1990618633","https://openalex.org/W2015587012","https://openalex.org/W2020513176","https://openalex.org/W2045652876","https://openalex.org/W2052435807","https://openalex.org/W2056382067","https://openalex.org/W2133602590","https://openalex.org/W2153918277","https://openalex.org/W2167831266","https://openalex.org/W2319466955","https://openalex.org/W4234426551"],"related_works":["https://openalex.org/W2058460798","https://openalex.org/W3005399847","https://openalex.org/W2381090488","https://openalex.org/W2392803409","https://openalex.org/W3165186662","https://openalex.org/W93000478","https://openalex.org/W2378915549","https://openalex.org/W1782792774","https://openalex.org/W2950227315","https://openalex.org/W2041455773"],"abstract_inverted_index":{"Systems":[0],"of":[1,40,66,91,95,105,109,111],"polynomial":[2,41,71],"equations":[3,42],"over":[4,46,81],"an":[5,53],"algebraically-closed":[6],"field":[7],"K":[8],"can":[9],"be":[10],"used":[11],"to":[12],"concisely":[13],"model":[14],"many":[15],"combinatorial":[16,22,58],"problems.":[17],"In":[18,48],"this":[19,49],"way,":[20],"a":[21,27,37,44],"problem":[23,90,101],"is":[24,29],"feasible":[25],"(e.g.,":[26],"graph":[28,100],"3-colorable,":[30],"hamiltonian,":[31],"etc.)":[32],"if":[33,36],"and":[34,76,107],"only":[35],"related":[38],"system":[39],"has":[43],"solution":[45],"K.":[47,82],"paper,":[50],"we":[51],"investigate":[52],"algorithm":[54],"aimed":[55],"at":[56],"proving":[57,92],"infeasibility":[59],"based":[60,87],"on":[61,77,85,88],"the":[62,89,93],"observed":[63],"low":[64],"degree":[65],"Hilbert's":[67],"Nullstellensatz":[68],"certificates":[69],"for":[70],"systems":[72],"arising":[73],"in":[74],"combinatorics":[75],"large-scale":[78],"linear-algebra":[79],"computations":[80],"We":[83,97],"report":[84],"experiments":[86],"non-3-colorability":[94],"graphs.":[96],"successfully":[98],"solved":[99],"instances":[102],"having":[103],"thousands":[104,110],"nodes":[106],"tens":[108],"edges.":[112]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":5}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
