{"id":"https://openalex.org/W2800189118","doi":"https://doi.org/10.37236/7903","title":"Unique Rectification in $d$-Complete Posets: Towards the $K$-Theory of Kac-Moody Flag Varieties","display_name":"Unique Rectification in $d$-Complete Posets: Towards the $K$-Theory of Kac-Moody Flag Varieties","publication_year":2018,"publication_date":"2018-10-19","ids":{"openalex":"https://openalex.org/W2800189118","doi":"https://doi.org/10.37236/7903","mag":"2800189118"},"language":"en","primary_location":{"id":"doi:10.37236/7903","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7903","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p19/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p19/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040251596","display_name":"Rahul Ilango","orcid":"https://orcid.org/0000-0002-0658-7813"},"institutions":[{"id":"https://openalex.org/I4210096112","display_name":"Rutgers Sexual and Reproductive Health and Rights","ror":"https://ror.org/00rcvgx40","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210096112"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Rahul Ilango","raw_affiliation_strings":["Rutgers University","Rutgers University *"],"affiliations":[{"raw_affiliation_string":"Rutgers University","institution_ids":["https://openalex.org/I4210096112"]},{"raw_affiliation_string":"Rutgers University *","institution_ids":["https://openalex.org/I4210096112"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058699487","display_name":"Oliver Pechenik","orcid":"https://orcid.org/0000-0002-7090-2072"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Oliver Pechenik","raw_affiliation_strings":["University of Michigan","\u2020University of Michigan"],"affiliations":[{"raw_affiliation_string":"University of Michigan","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"\u2020University of Michigan","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050694688","display_name":"Michael Zlatin","orcid":"https://orcid.org/0000-0003-1773-1152"},"institutions":[{"id":"https://openalex.org/I4210096112","display_name":"Rutgers Sexual and Reproductive Health and Rights","ror":"https://ror.org/00rcvgx40","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210096112"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Michael Zlatin","raw_affiliation_strings":["Rutgers University","Rutgers University *"],"affiliations":[{"raw_affiliation_string":"Rutgers University","institution_ids":["https://openalex.org/I4210096112"]},{"raw_affiliation_string":"Rutgers University *","institution_ids":["https://openalex.org/I4210096112"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040251596"],"corresponding_institution_ids":["https://openalex.org/I4210096112"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.1675996,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"25","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":1.0,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9991000294685364,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9980000257492065,"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/mathematics","display_name":"Mathematics","score":0.7719988226890564},{"id":"https://openalex.org/keywords/rectification","display_name":"Rectification","score":0.6628774404525757},{"id":"https://openalex.org/keywords/cohomology","display_name":"Cohomology","score":0.6417140364646912},{"id":"https://openalex.org/keywords/flag","display_name":"Flag (linear algebra)","score":0.6391087174415588},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5853437781333923},{"id":"https://openalex.org/keywords/structure-constants","display_name":"Structure constants","score":0.5357486605644226},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5137678384780884},{"id":"https://openalex.org/keywords/unification","display_name":"Unification","score":0.4201889932155609},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4166719317436218},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.333243191242218},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11539727449417114},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08395203948020935}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7719988226890564},{"id":"https://openalex.org/C50942859","wikidata":"https://www.wikidata.org/wiki/Q4967193","display_name":"Rectification","level":3,"score":0.6628774404525757},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.6417140364646912},{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.6391087174415588},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5853437781333923},{"id":"https://openalex.org/C2777394768","wikidata":"https://www.wikidata.org/wiki/Q7625098","display_name":"Structure constants","level":2,"score":0.5357486605644226},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5137678384780884},{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.4201889932155609},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4166719317436218},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.333243191242218},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11539727449417114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08395203948020935},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","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":3,"locations":[{"id":"doi:10.37236/7903","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7903","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p19/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"mag:2800189118","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1805.02287","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.1805.02287","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1805.02287","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-journal"}],"best_oa_location":{"id":"doi:10.37236/7903","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7903","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p19/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2800189118.pdf","grobid_xml":"https://content.openalex.org/works/W2800189118.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W371866709","https://openalex.org/W1546836223","https://openalex.org/W1967764902","https://openalex.org/W1975715897","https://openalex.org/W1985524664","https://openalex.org/W1999202617","https://openalex.org/W2030296624","https://openalex.org/W2043345731","https://openalex.org/W2059933353","https://openalex.org/W2060478591","https://openalex.org/W2082057393","https://openalex.org/W2087792692","https://openalex.org/W2109001550","https://openalex.org/W2110259507","https://openalex.org/W2117188922","https://openalex.org/W2135893164","https://openalex.org/W2270033890","https://openalex.org/W2607695981","https://openalex.org/W2751229218","https://openalex.org/W2759312131","https://openalex.org/W2912047518","https://openalex.org/W2964279988","https://openalex.org/W3104690264","https://openalex.org/W3105257694","https://openalex.org/W4247334960"],"related_works":["https://openalex.org/W2964040705","https://openalex.org/W2117188922","https://openalex.org/W2964341570","https://openalex.org/W3043118927","https://openalex.org/W2952865376","https://openalex.org/W1546836223","https://openalex.org/W2963653552","https://openalex.org/W2097267573","https://openalex.org/W2964279988","https://openalex.org/W2952791291","https://openalex.org/W3105622603","https://openalex.org/W2108703827","https://openalex.org/W1964512843","https://openalex.org/W2951589021","https://openalex.org/W2593404493","https://openalex.org/W2964051789","https://openalex.org/W2972635831","https://openalex.org/W2279151096","https://openalex.org/W3104493133"],"abstract_inverted_index":{"The":[0],"jeu-de-taquin-based":[1],"Littlewood-Richardson":[2],"rule":[3,58,83],"of":[4,31,47,74,91,101,110,118],"H.":[5],"Thomas":[6],"and":[7,39,67],"A.":[8,37],"Yong":[9],"(2009)":[10],"for":[11,130],"minuscule":[12,52,85],"varieties":[13,32,86],"has":[14],"been":[15],"extended":[16],"in":[17,51,114,136],"two":[18],"orthogonal":[19],"directions,":[20],"either":[21],"enriching":[22],"the":[23,29,56,72,81,99,108,137],"cohomology":[24,61],"theory":[25,46],"or":[26],"else":[27],"expanding":[28],"family":[30],"considered.":[33],"In":[34],"one":[35],"direction,":[36],"Buch":[38],"M.":[40],"Samuel":[41],"(2016)":[42],"developed":[43],"a":[44,88,115],"combinatorial":[45,128],"'unique":[48],"rectification":[49,112],"targets'":[50],"posets":[53],"to":[54,62,79,87,97],"extend":[55,80],"Thomas-Yong":[57,82],"from":[59,84],"ordinary":[60],"$K$-theory.":[63],"Separately,":[64],"P.-E.":[65],"Chaput":[66],"N.":[68],"Perrin":[69],"(2012)":[70],"used":[71],"combinatorics":[73],"R.":[75],"Proctor's":[76],"'$d$-complete":[77],"posets'":[78],"broader":[89],"class":[90,117],"Kac-Moody":[92,138],"structure":[93,134],"constants.":[94],"We":[95],"begin":[96],"address":[98],"unification":[100],"these":[102],"theories.":[103],"Our":[104],"main":[105],"result":[106],"is":[107],"existence":[109],"unique":[111],"targets":[113],"large":[116],"$d$-complete":[119],"posets.":[120],"From":[121],"this":[122],"result,":[123],"we":[124],"obtain":[125],"conjectural":[126],"positive":[127],"formulas":[129],"certain":[131],"$K$-theoretic":[132],"Schubert":[133],"constants":[135],"setting.":[139]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}