{"id":"https://openalex.org/W2140198698","doi":"https://doi.org/10.37236/1112","title":"Double Crystals of Binary and Integral Matrices","display_name":"Double Crystals of Binary and Integral Matrices","publication_year":2006,"publication_date":"2006-10-12","ids":{"openalex":"https://openalex.org/W2140198698","doi":"https://doi.org/10.37236/1112","mag":"2140198698"},"language":"en","primary_location":{"id":"doi:10.37236/1112","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1112","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r86/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/v13i1r86/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088555831","display_name":"Marc A. A. van Leeuwen","orcid":null},"institutions":[{"id":"https://openalex.org/I2802931824","display_name":"Institut Pprime","ror":"https://ror.org/05vjdsn22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171246369","https://openalex.org/I2802931824","https://openalex.org/I32881790","https://openalex.org/I4210095849"]},{"id":"https://openalex.org/I32881790","display_name":"Universit\u00e9 de Poitiers","ror":"https://ror.org/04xhy8q59","country_code":"FR","type":"education","lineage":["https://openalex.org/I32881790"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Marc A. A. Van Leeuwen","raw_affiliation_strings":["Universit de Poitiers, Dpartement de Mathmatiques, BP 30179, 86962 Futuroscope Chasseneuil Cedex, France","University of Poitiers"],"affiliations":[{"raw_affiliation_string":"Universit de Poitiers, Dpartement de Mathmatiques, BP 30179, 86962 Futuroscope Chasseneuil Cedex, France","institution_ids":["https://openalex.org/I2802931824","https://openalex.org/I32881790"]},{"raw_affiliation_string":"University of Poitiers","institution_ids":["https://openalex.org/I32881790"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088555831"],"corresponding_institution_ids":["https://openalex.org/I2802931824","https://openalex.org/I32881790"],"apc_list":null,"apc_paid":null,"fwci":0.4833,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.64738646,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","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":0.9986000061035156,"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":0.9986000061035156,"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":0.9919999837875366,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9889000058174133,"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":0.6853905916213989},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5980311632156372},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5509110689163208},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5412722229957581},{"id":"https://openalex.org/keywords/crystal","display_name":"Crystal (programming language)","score":0.49108433723449707},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4775317907333374},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41609442234039307},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1816011369228363},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1653040647506714},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1260961890220642},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.09403121471405029}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6853905916213989},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5980311632156372},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5509110689163208},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5412722229957581},{"id":"https://openalex.org/C2781285689","wikidata":"https://www.wikidata.org/wiki/Q21921428","display_name":"Crystal (programming language)","level":2,"score":0.49108433723449707},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4775317907333374},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41609442234039307},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1816011369228363},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1653040647506714},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1260961890220642},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.09403121471405029},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1112","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1112","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r86/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:10.37236/1112","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1112","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r86/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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2140198698.pdf","grobid_xml":"https://content.openalex.org/works/W2140198698.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W156450035","https://openalex.org/W1501196005","https://openalex.org/W1505854513","https://openalex.org/W1514829412","https://openalex.org/W1582044446","https://openalex.org/W1586417893","https://openalex.org/W1975605482","https://openalex.org/W2002495142","https://openalex.org/W2053554440","https://openalex.org/W2062537955","https://openalex.org/W2079430407","https://openalex.org/W2091216084","https://openalex.org/W2146590761","https://openalex.org/W2151016043","https://openalex.org/W2160916325","https://openalex.org/W2168316830","https://openalex.org/W2267867414","https://openalex.org/W2270010481","https://openalex.org/W2465291706","https://openalex.org/W2578021995","https://openalex.org/W2583196110","https://openalex.org/W2914659449","https://openalex.org/W2952350643","https://openalex.org/W4232463485","https://openalex.org/W4235393519","https://openalex.org/W4300302225","https://openalex.org/W6650920302"],"related_works":["https://openalex.org/W2046435967","https://openalex.org/W4231775656","https://openalex.org/W2980963558","https://openalex.org/W2383646825","https://openalex.org/W2371018915","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2,45,58,75,108,124,204,218,253],"set":[3],"of":[4,28,44,48,54,64,78,138,144,153,189,211,220,232,255,261,264,284],"operations":[5,10,84,91,97,135,161,182,202,272],"that":[6,270,277,292],"we":[7,251],"call":[8],"crystal":[9,46,90,134,160,201,233,271],"on":[11,51,61,186],"matrices":[12,140,265,285],"with":[13,33],"entries":[14],"either":[15],"in":[16,19,85,98,203,247,281],"$\\{0,1\\}$":[17],"or":[18,118],"$\\mathbf":[20],"N$.":[21],"There":[22],"are":[23],"horizontal":[24,131],"and":[25,36,68,71,150,196,222,238,267],"vertical":[26,133],"forms":[27],"these":[29,52],"operations,":[30],"which":[31],"commute":[32],"each":[34,137],"other,":[35],"they":[37,286],"give":[38],"rise":[39],"to":[40,89,93,103,148,207,241],"two":[41],"different":[42],"structures":[43],"graph":[47],"type":[49],"$A$":[50],"sets":[53],"matrices.":[55],"They":[56],"provide":[57],"new":[59,184],"perspective":[60],"many":[62],"aspects":[63],"the":[65,83,96,99,114,121,139,142,145,151,176,187,194,200,209,230,242,262,282,290],"RSK":[66,116,195],"correspondence":[67,178],"its":[69,119,239],"dual,":[70],"related":[72,197],"constructions.":[73],"Under":[74],"straightforward":[76],"encoding":[77,141],"semistandard":[79],"tableaux":[80,143],"by":[81,130],"matrices,":[82,212],"one":[86,213],"direction":[87,101],"correspond":[88,102],"applied":[92],"tableaux,":[94],"while":[95],"other":[100,243],"individual":[104],"moves":[105],"occurring":[106],"during":[107],"jeu":[109],"de":[110],"taquin":[111],"slide.":[112],"For":[113],"(dual)":[115],"correspondence,":[117,123,172],"variant":[120],"Burge":[122],"matrix":[125],"$M$":[126],"can":[127,156,165,226,287],"be":[128,157,167,227],"transformed":[129],"respectively":[132],"into":[136],"pair":[146],"associated":[147],"$M$,":[149],"inverse":[152],"this":[154,248],"decomposition":[155,164,210],"computed":[158],"using":[159],"too.":[162],"This":[163],"also":[166],"interpreted":[168],"as":[169,173,175,217],"computing":[170],"Robinson's":[171],"well":[174],"Robinson-Schensted":[177],"for":[179,192,259,278,297],"pictures.":[180],"Crystal":[181],"shed":[183],"light":[185],"method":[188,219],"growth":[190,215],"diagrams":[191,216],"describing":[193],"correspondences:":[198],"organising":[199],"particular":[205],"way":[206],"determine":[208],"finds":[214],"computation,":[221],"their":[223],"local":[224],"rules":[225],"deduced":[228],"from":[229],"definition":[231],"operations.":[234],"The":[235],"Sch\u00fctzenberger":[236],"involution":[237],"relation":[240],"correspondences":[244],"arise":[245],"naturally":[246],"context.":[249],"Finally":[250],"define":[252],"version":[254],"Greene's":[256],"poset":[257],"invariant":[258],"both":[260],"types":[263],"considered,":[266],"show":[268],"directly":[269],"leave":[273],"it":[274],"unchanged,":[275],"so":[276],"such":[279],"questions":[280],"setting":[283],"take":[288],"play":[289,296],"role":[291],"elementary":[293],"Knuth":[294],"transformations":[295],"words.":[298]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}
