{"id":"https://openalex.org/W2010743890","doi":"https://doi.org/10.1080/10586458.2007.10129009","title":"Tropical Polytopes and Cellular Resolutions","display_name":"Tropical Polytopes and Cellular Resolutions","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2010743890","doi":"https://doi.org/10.1080/10586458.2007.10129009","mag":"2010743890"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2007.10129009","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2007.10129009","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","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/A5085891249","display_name":"Mike Develin","orcid":null},"institutions":[{"id":"https://openalex.org/I1336492463","display_name":"American Institute of Mathematics","ror":"https://ror.org/02a0fwv66","country_code":"US","type":"funder","lineage":["https://openalex.org/I1311060795","https://openalex.org/I1336492463"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mike Develin","raw_affiliation_strings":["American Institute of Mathematics, 360 Portage Ave., Palo Alto, CA 94306"],"affiliations":[{"raw_affiliation_string":"American Institute of Mathematics, 360 Portage Ave., Palo Alto, CA 94306","institution_ids":["https://openalex.org/I1336492463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048333666","display_name":"Josephine Yu","orcid":"https://orcid.org/0000-0003-4962-3930"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Josephine Yu","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085891249"],"corresponding_institution_ids":["https://openalex.org/I1336492463"],"apc_list":null,"apc_paid":null,"fwci":6.0161,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.96836506,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"16","issue":"3","first_page":"277","last_page":"291"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9958999752998352,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9958999752998352,"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/polytope","display_name":"Polytope","score":0.9583114385604858},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8279315233230591},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.7794047594070435},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.578039288520813},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.5754976272583008},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5565791726112366},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.5225234031677246},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.497029572725296},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.49315208196640015},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.42775315046310425},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.42693349719047546},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3257473409175873},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08779224753379822},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0837772786617279}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9583114385604858},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8279315233230591},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.7794047594070435},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.578039288520813},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.5754976272583008},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5565791726112366},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.5225234031677246},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.497029572725296},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.49315208196640015},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.42775315046310425},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.42693349719047546},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3257473409175873},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08779224753379822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0837772786617279},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10586458.2007.10129009","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2007.10129009","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.em/1204928529","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1204928529","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.240.4488","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.240.4488","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0605494v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.240.5417","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.240.5417","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0605494v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/14","score":0.75,"display_name":"Life below water"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1968602707","https://openalex.org/W2025959085","https://openalex.org/W2144755471","https://openalex.org/W3037218708","https://openalex.org/W3037914599"],"related_works":["https://openalex.org/W2399505800","https://openalex.org/W333749553","https://openalex.org/W3121681491","https://openalex.org/W1966623661","https://openalex.org/W2942288111","https://openalex.org/W2951675266","https://openalex.org/W2467926385","https://openalex.org/W2039516134","https://openalex.org/W1653027350","https://openalex.org/W180925886"],"abstract_inverted_index":{"Tropical":[0],"polytopes":[1,5],"are":[2],"images":[3],"of":[4,26,29,37,46,56,65,68],"in":[6,53,91],"an":[7],"affine":[8],"space":[9],"over":[10],"the":[11,16,34,50,54],"Puiseux":[12],"series":[13],"field":[14],"under":[15],"degree":[17],"map.":[18],"This":[19],"viewpoint":[20],"gives":[21],"rise":[22],"to":[23],"a":[24,62,66,69],"family":[25],"cellular":[27],"resolutions":[28],"monomial":[30],"ideals":[31],"that":[32],"generalize":[33],"hull":[35,51],"complex":[36],"Bayer":[38],"and":[39,42,82,86],"Sturmfels":[40,43],"[Bayer":[41],"98],":[44],"instances":[45],"which":[47,72],"improve":[48],"upon":[49],"resolution":[52],"sense":[55],"being":[57],"smaller.":[58],"We":[59],"also":[60],"suggest":[61],"new":[63],"definition":[64],"face":[67],"tropical":[70],"polytope,":[71],"has":[73],"nicer":[74],"properties":[75],"than":[76],"previous":[77],"definitions;":[78],"we":[79],"give":[80],"examples":[81],"provide":[83],"many":[84],"conjectures":[85],"directions":[87],"for":[88],"further":[89],"research":[90],"this":[92],"area.":[93]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
