{"id":"https://openalex.org/W2078645519","doi":"https://doi.org/10.1016/s0747-7171(88)80043-9","title":"Standard bases and geometric invariant theoryI. Initial ideals and state polytopes","display_name":"Standard bases and geometric invariant theoryI. Initial ideals and state polytopes","publication_year":1988,"publication_date":"1988-10-01","ids":{"openalex":"https://openalex.org/W2078645519","doi":"https://doi.org/10.1016/s0747-7171(88)80043-9","mag":"2078645519"},"language":"en","primary_location":{"id":"doi:10.1016/s0747-7171(88)80043-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(88)80043-9","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-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/A5109961209","display_name":"David Bayer","orcid":"https://orcid.org/0009-0008-1805-0045"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David Bayer","raw_affiliation_strings":["Department of Mathematics, Columbia University, New York, NY 10027, U.S.A","Department of Mathematics Columbia University New York, NY 10027, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Columbia University, New York, NY 10027, U.S.A","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Department of Mathematics Columbia University New York, NY 10027, U.S.A","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079109740","display_name":"Ian Morrison","orcid":null},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ian Morrison","raw_affiliation_strings":["Department of Mathematics, Columbia University, New York, NY 10027, U.S.A","Department of Mathematics Columbia University New York, NY 10027, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Columbia University, New York, NY 10027, U.S.A","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Department of Mathematics Columbia University New York, NY 10027, U.S.A","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109961209"],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":{"value":2770,"currency":"USD","value_usd":2770},"apc_paid":null,"fwci":1.6506,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.85553471,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"6","issue":"2-3","first_page":"209","last_page":"217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9998999834060669,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9998999834060669,"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":0.9980999827384949,"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":0.9936000108718872,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9141335487365723},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8288972973823547},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.820854902267456},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.6868411898612976},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5975732207298279},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5951534509658813},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.5605601668357849},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47021913528442383},{"id":"https://openalex.org/keywords/hilbert-series-and-hilbert-polynomial","display_name":"Hilbert series and Hilbert polynomial","score":0.4373829662799835},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3807924687862396},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3752775490283966},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28724193572998047},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.21056857705116272},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10636904835700989},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09236353635787964}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9141335487365723},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8288972973823547},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.820854902267456},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6868411898612976},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5975732207298279},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5951534509658813},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.5605601668357849},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47021913528442383},{"id":"https://openalex.org/C57033185","wikidata":"https://www.wikidata.org/wiki/Q5761236","display_name":"Hilbert series and Hilbert polynomial","level":3,"score":0.4373829662799835},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3807924687862396},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3752775490283966},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28724193572998047},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.21056857705116272},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10636904835700989},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09236353635787964},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0747-7171(88)80043-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(88)80043-9","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.368.4093","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.368.4093","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uga.edu/~davids/S2AM/BayerMorrison1988.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4399999976158142,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1505369303","https://openalex.org/W1515224754","https://openalex.org/W1524190946","https://openalex.org/W1572341022","https://openalex.org/W1635682819","https://openalex.org/W1781640942","https://openalex.org/W1784574365","https://openalex.org/W1963695291","https://openalex.org/W1982438618","https://openalex.org/W1991262648","https://openalex.org/W1992838187","https://openalex.org/W2018615018","https://openalex.org/W2026853928","https://openalex.org/W2189005442","https://openalex.org/W6630274136","https://openalex.org/W6630786544","https://openalex.org/W6631336743","https://openalex.org/W6634102986","https://openalex.org/W6638215453","https://openalex.org/W6655185796"],"related_works":["https://openalex.org/W2963281686","https://openalex.org/W3217635579","https://openalex.org/W2086266104","https://openalex.org/W1604878022","https://openalex.org/W3014934786","https://openalex.org/W2007005467","https://openalex.org/W2078645519","https://openalex.org/W1500873744","https://openalex.org/W2392587207","https://openalex.org/W2025539184"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-22T08:38:42.863108","created_date":"2025-10-10T00:00:00"}
