{"id":"https://openalex.org/W2993985424","doi":"https://doi.org/10.37236/84","title":"Affine Partitions and Affine Grassmannians","display_name":"Affine Partitions and Affine Grassmannians","publication_year":2009,"publication_date":"2009-07-02","ids":{"openalex":"https://openalex.org/W2993985424","doi":"https://doi.org/10.37236/84","mag":"2993985424"},"language":"en","primary_location":{"id":"doi:10.37236/84","is_oa":true,"landing_page_url":"https://doi.org/10.37236/84","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i2r18/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i2r18/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090924793","display_name":"Sara Billey","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sara C. Billey","raw_affiliation_strings":["Department of Mathematics University of Washington Seattle, WA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Washington Seattle, WA","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045073307","display_name":"Stephen \u0391. Mitchell","orcid":"https://orcid.org/0000-0002-1468-7558"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen A. Mitchell","raw_affiliation_strings":["Department of Mathematics University of Washington Seattle, WA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Washington Seattle, WA","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090924793"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":null,"apc_paid":null,"fwci":2.3671,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.88147892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"2","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":0.9998000264167786,"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":0.9998000264167786,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9980999827384949,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8455651998519897},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.8025299906730652},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7628834247589111},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6606053113937378},{"id":"https://openalex.org/keywords/affine-representation","display_name":"Affine representation","score":0.4839663803577423},{"id":"https://openalex.org/keywords/bruhat-order","display_name":"Bruhat order","score":0.46878206729888916},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.45745623111724854},{"id":"https://openalex.org/keywords/weyl-group","display_name":"Weyl group","score":0.45644715428352356},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.44277578592300415},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.44169652462005615},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4404081404209137},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.41744890809059143},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3277263045310974},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2075788974761963},{"id":"https://openalex.org/keywords/affine-lie-algebra","display_name":"Affine Lie algebra","score":0.10387656092643738}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8455651998519897},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8025299906730652},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7628834247589111},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6606053113937378},{"id":"https://openalex.org/C6128414","wikidata":"https://www.wikidata.org/wiki/Q3892887","display_name":"Affine representation","level":5,"score":0.4839663803577423},{"id":"https://openalex.org/C177274530","wikidata":"https://www.wikidata.org/wiki/Q4978697","display_name":"Bruhat order","level":3,"score":0.46878206729888916},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.45745623111724854},{"id":"https://openalex.org/C40233952","wikidata":"https://www.wikidata.org/wiki/Q768074","display_name":"Weyl group","level":2,"score":0.45644715428352356},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.44277578592300415},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.44169652462005615},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4404081404209137},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.41744890809059143},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3277263045310974},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2075788974761963},{"id":"https://openalex.org/C5475112","wikidata":"https://www.wikidata.org/wiki/Q632521","display_name":"Affine Lie algebra","level":4,"score":0.10387656092643738},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C81999800","wikidata":"https://www.wikidata.org/wiki/Q1454725","display_name":"Current algebra","level":3,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/84","is_oa":true,"landing_page_url":"https://doi.org/10.37236/84","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i2r18/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/84","is_oa":true,"landing_page_url":"https://doi.org/10.37236/84","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i2r18/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2993985424.pdf","grobid_xml":"https://content.openalex.org/works/W2993985424.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W35421105","https://openalex.org/W112671161","https://openalex.org/W138218393","https://openalex.org/W191345121","https://openalex.org/W1553824818","https://openalex.org/W1821668736","https://openalex.org/W1920048536","https://openalex.org/W1983441137","https://openalex.org/W2006167109","https://openalex.org/W2009190506","https://openalex.org/W2045528550","https://openalex.org/W2070626515","https://openalex.org/W2077148545","https://openalex.org/W2086682269","https://openalex.org/W2102201301","https://openalex.org/W2125838758","https://openalex.org/W2130348363","https://openalex.org/W2138089388","https://openalex.org/W2315398081","https://openalex.org/W2914659449","https://openalex.org/W2950828983","https://openalex.org/W2993737986","https://openalex.org/W3098748469","https://openalex.org/W4239506166","https://openalex.org/W4251669121","https://openalex.org/W4310661226","https://openalex.org/W6601795639","https://openalex.org/W6603593799","https://openalex.org/W6605693991","https://openalex.org/W6610610092","https://openalex.org/W6612833668","https://openalex.org/W6794281356"],"related_works":["https://openalex.org/W2046528973","https://openalex.org/W2949497458","https://openalex.org/W2950747717","https://openalex.org/W3170345835","https://openalex.org/W2971824022","https://openalex.org/W3098953809","https://openalex.org/W3114738300","https://openalex.org/W4300725824","https://openalex.org/W2469437700","https://openalex.org/W3159771067"],"abstract_inverted_index":{"We":[0],"give":[1,29],"a":[2,102,113],"bijection":[3,74],"between":[4],"certain":[5,36],"colored":[6,27,65],"partitions":[7,28,66,77,100],"and":[8,49,78,101,111],"the":[9,12,44,54,63,87,93,120],"elements":[10],"in":[11,43,73,92,96],"quotient":[13],"of":[14,46,70,98,104,115,119],"an":[15],"affine":[16,64,94,99],"Weyl":[17,21],"group":[18],"modulo":[19],"its":[20],"group.":[22],"By":[23],"Bott's":[24],"formula":[25],"these":[26,38],"rise":[30],"to":[31,57,85],"some":[32],"partition":[33],"identities.":[34],"In":[35,51],"types,":[37],"identities":[39,55],"have":[40],"previously":[41],"appeared":[42],"work":[45],"Bousquet-Melou-Eriksson,":[47],"Eriksson-Eriksson":[48],"Reiner.":[50],"other":[52],"types":[53],"appear":[56],"be":[58],"new.":[59],"For":[60],"type":[61],"$A_{n}$,":[62],"form":[67],"another":[68],"family":[69],"combinatorial":[71],"objects":[72],"with":[75],"$(n+1)$-core":[76],"$n$-bounded":[79],"partitions.":[80],"Our":[81],"main":[82],"application":[83],"is":[84,112],"characterize":[86],"rationally":[88],"smooth":[89],"Schubert":[90],"varieties":[91],"Grassmannians":[95],"terms":[97],"generalization":[103],"Young's":[105],"lattice":[106],"which":[107],"refines":[108],"weak":[109],"order":[110],"subposet":[114],"Bruhat":[116],"order.":[117],"Several":[118],"proofs":[121],"are":[122],"computer":[123],"assisted.":[124]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
