{"id":"https://openalex.org/W4235434555","doi":"https://doi.org/10.37236/1554","title":"The Skeleton of a Reduced Word and a Correspondence of Edelman and Greene","display_name":"The Skeleton of a Reduced Word and a Correspondence of Edelman and Greene","publication_year":2000,"publication_date":"2000-12-29","ids":{"openalex":"https://openalex.org/W4235434555","doi":"https://doi.org/10.37236/1554"},"language":"en","primary_location":{"id":"doi:10.37236/1554","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1554","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r10/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r10/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005468020","display_name":"Stefan Felsner","orcid":"https://orcid.org/0000-0002-6150-1998"},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Stefan Felsner","raw_affiliation_strings":["Freie Universitt Berlin Fachbereich Mathematik und Informatik Takustr. 9 14195 Berlin, Germany","Freie Universit\u00e4t Berlin Fachbereich Mathematik und Informatik Takustr. 9 14195 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Freie Universitt Berlin Fachbereich Mathematik und Informatik Takustr. 9 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Freie Universit\u00e4t Berlin Fachbereich Mathematik und Informatik Takustr. 9 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005468020"],"corresponding_institution_ids":["https://openalex.org/I75951250"],"apc_list":null,"apc_paid":null,"fwci":0.6548,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7080292,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"1","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/T11567","display_name":"semigroups and automata theory","score":0.9994999766349792,"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/T11130","display_name":"Coding theory and cryptography","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/bijection","display_name":"Bijection","score":0.8064398765563965},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7973164916038513},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7713348865509033},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7642720937728882},{"id":"https://openalex.org/keywords/young-tableau","display_name":"Young tableau","score":0.7012616991996765},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.6695886850357056},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.641260027885437},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6083436608314514},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5828569531440735},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.10796105861663818},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10434362292289734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0735028088092804}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8064398765563965},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7973164916038513},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7713348865509033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7642720937728882},{"id":"https://openalex.org/C165368118","wikidata":"https://www.wikidata.org/wiki/Q2166280","display_name":"Young tableau","level":2,"score":0.7012616991996765},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.6695886850357056},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.641260027885437},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6083436608314514},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5828569531440735},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.10796105861663818},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10434362292289734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0735028088092804},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C107038049","wikidata":"https://www.wikidata.org/wiki/Q35986","display_name":"Aesthetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1554","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1554","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r10/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":false,"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:10.37236/1554","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1554","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r10/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":false,"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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4235434555.pdf","grobid_xml":"https://content.openalex.org/works/W4235434555.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1551177513","https://openalex.org/W1970679756","https://openalex.org/W1995154714","https://openalex.org/W2035440108","https://openalex.org/W2075581822","https://openalex.org/W2158525989","https://openalex.org/W2168316830","https://openalex.org/W2505205968","https://openalex.org/W4235434555","https://openalex.org/W6602670373","https://openalex.org/W6633749307","https://openalex.org/W6636979980","https://openalex.org/W6697549010"],"related_works":["https://openalex.org/W4287266902","https://openalex.org/W1524776069","https://openalex.org/W2950642020","https://openalex.org/W1721535522","https://openalex.org/W2952981421","https://openalex.org/W2558105755","https://openalex.org/W2900158650","https://openalex.org/W2258229947","https://openalex.org/W2799131975","https://openalex.org/W4302779826"],"abstract_inverted_index":{"Stanley":[0,60],"conjectured":[1],"that":[2],"the":[3,9,17,23,26,34,78,94,97,113,119,122,125],"number":[4,18,35],"of":[5,13,19,22,25,36,40,77,87,96,112],"maximal":[6],"chains":[7],"in":[8],"weak":[10],"Bruhat":[11],"order":[12],"$S_n$,":[14],"or":[15],"equivalently":[16],"reduced":[20,55],"decompositions":[21],"reverse":[24],"identity":[27],"permutation":[28],"$":[29],"w_0":[30],"=":[31],"n,n-1,n-2,\\ldots,2,1$,":[32],"equals":[33],"standard":[37,51],"Young":[38,52],"tableaux":[39,53],"staircase":[41],"shape":[42],"$s=\\{n-1,n-2,\\ldots,1\\}$.":[43],"Originating":[44],"from":[45],"this":[46],"conjecture":[47,63],"remarkable":[48],"connections":[49],"between":[50],"and":[54,67,80,132],"words":[56],"have":[57,128],"been":[58],"discovered.":[59],"proved":[61],"his":[62],"algebraically,":[64],"later":[65],"Edelman":[66,79],"Greene":[68,81],"found":[69],"a":[70,84],"bijective":[71],"proof.":[72],"We":[73],"provide":[74],"an":[75],"extension":[76,90,95],"bijection":[82],"to":[83,93,100],"larger":[85],"class":[86],"words.":[88],"This":[89],"is":[91,106,118],"similar":[92],"Robinson-Schensted":[98,114],"correspondence":[99,124],"two":[101],"line":[102],"arrays.":[103],"Our":[104],"proof":[105,111],"inspired":[107],"by":[108],"Viennot's":[109],"planarized":[110,126],"correspondence.":[115],"As":[116],"it":[117],"case":[120],"with":[121],"classical":[123],"proofs":[127],"their":[129],"own":[130],"beauty":[131],"simplicity.":[133]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}