{"id":"https://openalex.org/W2077569399","doi":"https://doi.org/10.1145/1576702.1576716","title":"Lower bounds for zero-dimensional projections","display_name":"Lower bounds for zero-dimensional projections","publication_year":2009,"publication_date":"2009-07-28","ids":{"openalex":"https://openalex.org/W2077569399","doi":"https://doi.org/10.1145/1576702.1576716","mag":"2077569399"},"language":"en","primary_location":{"id":"doi:10.1145/1576702.1576716","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576716","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 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/A5053061243","display_name":"W. Dale Brownawell","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"W. Dale Brownawell","raw_affiliation_strings":["Penn State University, University Park, PA, USA",", Penn State University, University Park, PA, USA"],"affiliations":[{"raw_affiliation_string":"Penn State University, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":", Penn State University, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078989577","display_name":"Chee Yap","orcid":"https://orcid.org/0000-0003-2952-3545"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chee K. Yap","raw_affiliation_strings":["Courant Institute, New York University, New York, NY, USA","Courant Institute, New York University, New York, NY, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Courant Institute, New York University, New York, NY, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Courant Institute, New York University, New York, NY, USA#TAB#","institution_ids":["https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053061243"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":3.1021,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.91491023,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"79","last_page":"86"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9991999864578247,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9986000061035156,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9977999925613403,"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/zero","display_name":"Zero (linguistics)","score":0.6284900307655334},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4506537914276123},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35708725452423096},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.0627981424331665}],"concepts":[{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6284900307655334},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4506537914276123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35708725452423096},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0627981424331665},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1576702.1576716","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576716","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 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.603.5416","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.603.5416","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.nyu.edu/exact/doc/zero-bound-proj.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W200176247","https://openalex.org/W1481724961","https://openalex.org/W1488976814","https://openalex.org/W1496801598","https://openalex.org/W1501243125","https://openalex.org/W1506764403","https://openalex.org/W1529743226","https://openalex.org/W1964839258","https://openalex.org/W1976392590","https://openalex.org/W1978491945","https://openalex.org/W1981238134","https://openalex.org/W1983321700","https://openalex.org/W1983469327","https://openalex.org/W1986405515","https://openalex.org/W1988839605","https://openalex.org/W2012369998","https://openalex.org/W2025941018","https://openalex.org/W2037615924","https://openalex.org/W2042650700","https://openalex.org/W2062258004","https://openalex.org/W2063118073","https://openalex.org/W2065139236","https://openalex.org/W2066092589","https://openalex.org/W2084459701","https://openalex.org/W2124925673","https://openalex.org/W2132710642","https://openalex.org/W2140258961","https://openalex.org/W2156153879","https://openalex.org/W2156616818","https://openalex.org/W2164167093","https://openalex.org/W2609774945","https://openalex.org/W2970485886","https://openalex.org/W4205241946","https://openalex.org/W4231022671","https://openalex.org/W4238665603","https://openalex.org/W4244593923","https://openalex.org/W4248594911","https://openalex.org/W4301746773"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694"],"abstract_inverted_index":{"Let":[0],"I":[1],"be":[2,15],"an":[3,16],"ideal":[4],"generated":[5],"by":[6],"polynomials":[7],"P1,...,":[8],"Pm":[9],"\u2208":[10,42],"Z[X1,...,":[11],"Xn],":[12],"and":[13,37,61,66,74],"P":[14],"isolated":[17],"prime":[18],"component":[19],"of":[20,25,59,70],"I.":[21],"If":[22],"the":[23,30,62,71],"projection":[24],"Zero(P)":[26,43],"\u2286":[27],"Cn":[28],"onto":[29],"first":[31],"coordinate":[32],"is":[33],"a":[34,51],"finite":[35],"set,":[36],"\u03b6":[38],"=":[39],"(\u03b61,...,":[40],"\u03b6n)":[41],"where":[44],"\u03b61":[45],"6=":[46],"0,":[47],"then":[48],"we":[49],"prove":[50],"lower":[52],"bound":[53],"on":[54],"|\u03b61":[55],"|":[56],"in":[57],"terms":[58],"n,m":[60],"maximum":[63,67],"degree":[64],"D":[65],"height":[68],"H":[69],"polynomials.":[72],"Categories":[73],"Subject":[75],"Descriptors":[76]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}