{"id":"https://openalex.org/W2143746847","doi":"https://doi.org/10.1145/1837934.1837971","title":"Solving schubert problems with Littlewood-Richardson homotopies","display_name":"Solving schubert problems with Littlewood-Richardson homotopies","publication_year":2010,"publication_date":"2010-07-25","ids":{"openalex":"https://openalex.org/W2143746847","doi":"https://doi.org/10.1145/1837934.1837971","mag":"2143746847"},"language":"en","primary_location":{"id":"doi:10.1145/1837934.1837971","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837971","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 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/A5078229263","display_name":"Frank Sottile","orcid":"https://orcid.org/0000-0003-0087-7120"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Frank Sottile","raw_affiliation_strings":["Texas A&amp;M University, College Station, TX","Texas A&M University, College Station. TX#TAB#"],"affiliations":[{"raw_affiliation_string":"Texas A&amp;M University, College Station, TX","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Texas A&M University, College Station. TX#TAB#","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013856193","display_name":"Ravi Vakil","orcid":"https://orcid.org/0000-0001-8506-270X"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ravi Vakil","raw_affiliation_strings":["Stanford University, Stanford, CA"],"affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, CA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112224754","display_name":"Jan Verschelde","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jan Verschelde","raw_affiliation_strings":["University of Illinois at Chicago, Chicago, IL"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Chicago, Chicago, IL","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078229263"],"corresponding_institution_ids":["https://openalex.org/I91045830"],"apc_list":null,"apc_paid":null,"fwci":1.0036,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.78013471,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"179","last_page":"186"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9987999796867371,"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":0.9987999796867371,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.97079998254776,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.6033458709716797},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5623581409454346},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5272549390792847},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.5266711115837097},{"id":"https://openalex.org/keywords/schubert-calculus","display_name":"Schubert calculus","score":0.44505441188812256},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4296703040599823},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39763686060905457},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3629341423511505},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1953643262386322}],"concepts":[{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.6033458709716797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5623581409454346},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5272549390792847},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.5266711115837097},{"id":"https://openalex.org/C169843257","wikidata":"https://www.wikidata.org/wiki/Q7432936","display_name":"Schubert calculus","level":3,"score":0.44505441188812256},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4296703040599823},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39763686060905457},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3629341423511505},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1953643262386322},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1837934.1837971","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837971","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4013022459","display_name":null,"funder_award_id":"DMS-0538734DMS-0915211DMS-0801196DMS-0713018","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W18833213","https://openalex.org/W1570420806","https://openalex.org/W1676075617","https://openalex.org/W1965520434","https://openalex.org/W1974806647","https://openalex.org/W1988076923","https://openalex.org/W2028576930","https://openalex.org/W2041734651","https://openalex.org/W2042438690","https://openalex.org/W2043380031","https://openalex.org/W2057706156","https://openalex.org/W2075349905","https://openalex.org/W2087834874","https://openalex.org/W2109001550","https://openalex.org/W2109596995","https://openalex.org/W2114827489","https://openalex.org/W2120055796","https://openalex.org/W2121306562","https://openalex.org/W2134357230","https://openalex.org/W2144273467","https://openalex.org/W2159461250","https://openalex.org/W2318524654"],"related_works":["https://openalex.org/W2030296624","https://openalex.org/W2391752819","https://openalex.org/W4297579280","https://openalex.org/W2021311057","https://openalex.org/W2015757695","https://openalex.org/W2362256999","https://openalex.org/W2007245702","https://openalex.org/W2048873866","https://openalex.org/W4298169709","https://openalex.org/W3097240163"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,43,57],"new":[3],"numerical":[4],"homotopy":[5,19,74],"continuation":[6],"algorithm":[7,75],"for":[8],"finding":[9],"all":[10],"solutions":[11,32,55],"to":[12,52,56],"Schubert":[13,59,63],"problems":[14,64],"on":[15,22],"Grassmannians.":[16],"This":[17],"Littlewood-Richardson":[18,28,73],"is":[20,70,76],"based":[21],"Vakil's":[23],"geometric":[24],"proof":[25],"of":[26,45,67,82],"the":[27,54,65,79,83],"rule.":[29],"Its":[30],"start":[31],"are":[33,40],"given":[34,58],"by":[35,48],"linear":[36],"equations":[37],"and":[38],"they":[39],"tracked":[41,69],"through":[42],"sequence":[44],"homotopies":[46],"encoded":[47],"certain":[49],"checker":[50],"configurations":[51],"find":[53],"problem.":[60],"For":[61],"generic":[62],"number":[66],"paths":[68],"optimal.":[71],"The":[72],"implemented":[77],"using":[78],"path":[80],"trackers":[81],"software":[84],"package":[85],"PHCpack.":[86]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
