{"id":"https://openalex.org/W2595235157","doi":"https://doi.org/10.1137/17m1160148","title":"Khovanskii Bases, Higher Rank Valuations, and Tropical Geometry","display_name":"Khovanskii Bases, Higher Rank Valuations, and Tropical Geometry","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2595235157","doi":"https://doi.org/10.1137/17m1160148","mag":"2595235157"},"language":"en","primary_location":{"id":"doi:10.1137/17m1160148","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1160148","pdf_url":null,"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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1610.00298","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069477356","display_name":"Kiumars Kaveh","orcid":"https://orcid.org/0000-0002-7251-732X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kiumars Kaveh","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7251-732X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5069339031","display_name":"Christopher Manon","orcid":"https://orcid.org/0000-0003-3285-6375"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christopher Manon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069477356"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2801,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.86630457,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"3","issue":"2","first_page":"292","last_page":"336"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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/mathematics","display_name":"Mathematics","score":0.8295314908027649},{"id":"https://openalex.org/keywords/tropical-geometry","display_name":"Tropical geometry","score":0.6795141696929932},{"id":"https://openalex.org/keywords/compactification","display_name":"Compactification (mathematics)","score":0.600521981716156},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5748043656349182},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.48428434133529663},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.4524296224117279},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.44671061635017395},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.44082513451576233},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.43609267473220825},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25625520944595337},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24620983004570007}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8295314908027649},{"id":"https://openalex.org/C202652594","wikidata":"https://www.wikidata.org/wiki/Q2982669","display_name":"Tropical geometry","level":2,"score":0.6795141696929932},{"id":"https://openalex.org/C2779165322","wikidata":"https://www.wikidata.org/wiki/Q546145","display_name":"Compactification (mathematics)","level":2,"score":0.600521981716156},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5748043656349182},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.48428434133529663},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.4524296224117279},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.44671061635017395},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44082513451576233},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.43609267473220825},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25625520944595337},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24620983004570007}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1160148","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1160148","pdf_url":null,"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:arXiv.org:1610.00298","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.00298","pdf_url":"https://arxiv.org/pdf/1610.00298","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":"mag:2595235157","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1610.00298.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1610.00298","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1610.00298","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1610.00298","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.00298","pdf_url":"https://arxiv.org/pdf/1610.00298","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5478042332","display_name":null,"funder_award_id":"DMS-1601303","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5684916873","display_name":"Convex Bodies, Algebraic Geometry, and Symplectic Geometry","funder_award_id":"1601303","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6191432922","display_name":"Enumeration Problems in Algebraic Geometry and Representation Theory","funder_award_id":"1500966","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8163374094","display_name":null,"funder_award_id":"DMS-1500966","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/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2595235157.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1523097020","https://openalex.org/W1656386701","https://openalex.org/W1795560854","https://openalex.org/W1909207196","https://openalex.org/W1967804849","https://openalex.org/W1968936725","https://openalex.org/W1989312182","https://openalex.org/W2012810097","https://openalex.org/W2013989688","https://openalex.org/W2020261115","https://openalex.org/W2047789112","https://openalex.org/W2050626380","https://openalex.org/W2063835872","https://openalex.org/W2079988604","https://openalex.org/W2087834874","https://openalex.org/W2104713530","https://openalex.org/W2123877559","https://openalex.org/W2150599797","https://openalex.org/W2160328340","https://openalex.org/W2171319959","https://openalex.org/W2171860168","https://openalex.org/W2284330248","https://openalex.org/W2408970639","https://openalex.org/W2554108551","https://openalex.org/W2765832835","https://openalex.org/W2771406229","https://openalex.org/W2951816119","https://openalex.org/W2962941672","https://openalex.org/W2963114720","https://openalex.org/W2963135445","https://openalex.org/W2963344595","https://openalex.org/W2963674602","https://openalex.org/W2963955986","https://openalex.org/W2964023259","https://openalex.org/W2964220995","https://openalex.org/W2964298682","https://openalex.org/W2973308022","https://openalex.org/W3037209219","https://openalex.org/W3104017638","https://openalex.org/W4252077841"],"related_works":["https://openalex.org/W2013989688","https://openalex.org/W2964023259","https://openalex.org/W2079988604","https://openalex.org/W2963164288","https://openalex.org/W2771406229","https://openalex.org/W2889768548","https://openalex.org/W3184718659","https://openalex.org/W2950552322","https://openalex.org/W1842093916","https://openalex.org/W3034590356","https://openalex.org/W3206356186","https://openalex.org/W2625025761","https://openalex.org/W2899809953","https://openalex.org/W787922409","https://openalex.org/W2013824808","https://openalex.org/W2531540505","https://openalex.org/W3104848027","https://openalex.org/W2969632132","https://openalex.org/W2122765776","https://openalex.org/W2336061216"],"abstract_inverted_index":{"Given":[0],"a":[1,8,14,28,52,59,78],"finitely":[2,22,71],"generated":[3,23,72],"algebra":[4],"$A$,":[5],"it":[6],"is":[7],"fundamental":[9],"question":[10],"whether":[11],"$A$":[12],"has":[13],"full":[15],"rank":[16],"discrete":[17],"(Krull)":[18],"valuation":[19],"$\\mathfrak{v}$":[20],"with":[21],"value":[24],"semigroup.":[25],"We":[26,97,130],"give":[27],"necessary":[29],"and":[30,87,90],"sufficient":[31],"condition":[32],"for":[33,55,61],"this":[34,46,76],"in":[35,94],"terms":[36],"of":[37,40,45,51,84,103,116,119,127],"tropical":[38,88],"geometry":[39],"$A$.":[41],"In":[42,74],"the":[43,49,82,113],"course":[44],"we":[47],"introduce":[48],"notion":[50],"Khovanskii":[53],"basis":[54],"$(A,\\mathfrak{v})$":[56],"which":[57],"provides":[58],"framework":[60],"far":[62],"extending":[63],"Gr\u00f6bner":[64],"theory":[65,83],"on":[66],"polynomial":[67],"algebras":[68,138],"to":[69],"general":[70],"algebras.":[73],"particular,":[75],"makes":[77],"direct":[79],"connection":[80],"between":[81],"Newton--Okounkov":[85],"bodies":[86],"geometry,":[89],"toric":[91],"degenerations":[92,115],"arising":[93],"both":[95],"contexts.":[96],"also":[98],"construct":[99],"an":[100],"associated":[101],"compactification":[102],"${Spec}\\,(A)$.":[104],"Our":[105],"approach":[106],"includes":[107],"many":[108,133],"familiar":[109],"examples":[110,134],"such":[111],"as":[112,122,124],"Gel'fand--Zetlin":[114],"coordinate":[117],"rings":[118],"flag":[120],"varieties":[121],"well":[123],"wonderful":[125],"compactifications":[126],"reductive":[128],"groups.":[129],"expect":[131],"that":[132],"coming":[135],"from":[136],"cluster":[137],"naturally":[139],"fit":[140],"into":[141],"our":[142],"framework.":[143]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
