{"id":"https://openalex.org/W2108773821","doi":"https://doi.org/10.37236/4335","title":"Iterative Properties of Birational Rowmotion II: Rectangles and Triangles","display_name":"Iterative Properties of Birational Rowmotion II: Rectangles and Triangles","publication_year":2015,"publication_date":"2015-09-20","ids":{"openalex":"https://openalex.org/W2108773821","doi":"https://doi.org/10.37236/4335","mag":"2108773821"},"language":"en","primary_location":{"id":"doi:10.37236/4335","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4335","pdf_url":null,"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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/4335","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074897310","display_name":"Darij Grinberg","orcid":"https://orcid.org/0000-0002-9661-8432"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Darij Grinberg","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071443532","display_name":"Tom Roby","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tom Roby","raw_affiliation_strings":["University of Connecticut"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Connecticut","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.089,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.9689942,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"22","issue":"3","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":0.9998999834060669,"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":0.9998999834060669,"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":0.9997000098228455,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9987999796867371,"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/partially-ordered-set","display_name":"Partially ordered set","score":0.9096184968948364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8507372140884399},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6635554432868958},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6240805387496948},{"id":"https://openalex.org/keywords/cluster-algebra","display_name":"Cluster algebra","score":0.6046066284179688},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.5628880858421326},{"id":"https://openalex.org/keywords/star-product","display_name":"Star product","score":0.5469940900802612},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5281736254692078},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5066245198249817},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.48784732818603516},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.48041534423828125},{"id":"https://openalex.org/keywords/maximal-element","display_name":"Maximal element","score":0.4637938141822815},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40255314111709595},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3949242830276489},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08533802628517151}],"concepts":[{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.9096184968948364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8507372140884399},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6635554432868958},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6240805387496948},{"id":"https://openalex.org/C165879259","wikidata":"https://www.wikidata.org/wiki/Q5136690","display_name":"Cluster algebra","level":3,"score":0.6046066284179688},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.5628880858421326},{"id":"https://openalex.org/C195800304","wikidata":"https://www.wikidata.org/wiki/Q7601281","display_name":"Star product","level":2,"score":0.5469940900802612},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5281736254692078},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5066245198249817},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.48784732818603516},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.48041534423828125},{"id":"https://openalex.org/C196773441","wikidata":"https://www.wikidata.org/wiki/Q1475294","display_name":"Maximal element","level":3,"score":0.4637938141822815},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40255314111709595},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3949242830276489},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08533802628517151},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/4335","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4335","pdf_url":null,"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":"pmh:oai:dspace.mit.edu:1721.1/100753","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/100753","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"European Mathematical Information Service (EMIS)","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"doi:10.37236/4335","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4335","pdf_url":null,"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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1579213680","https://openalex.org/W1672638072","https://openalex.org/W1977467370","https://openalex.org/W2006159741","https://openalex.org/W2029308197","https://openalex.org/W2031564163","https://openalex.org/W2042537647","https://openalex.org/W2055669112","https://openalex.org/W2078602696","https://openalex.org/W2117593827","https://openalex.org/W2128103201","https://openalex.org/W2130710312","https://openalex.org/W2151016043"],"related_works":["https://openalex.org/W3033029084","https://openalex.org/W4254064397","https://openalex.org/W2957182409","https://openalex.org/W4288282388","https://openalex.org/W3143802155","https://openalex.org/W2015965805","https://openalex.org/W2789323833","https://openalex.org/W1854642140","https://openalex.org/W2108773821","https://openalex.org/W1986027645"],"abstract_inverted_index":{"Birational":[0],"rowmotion":[1,28,148],"\u2014":[2,12],"a":[3,21,64,68,94,109,112],"birational":[4,43,147],"map":[5,29],"associated":[6],"to":[7,87,131,157,169],"any":[8],"finite":[9,89,102,113,144],"poset":[10,58,123],"$P$":[11],"has":[13,49],"been":[14],"introduced":[15,127],"by":[16,128],"Einstein":[17],"and":[18],"Propp":[19],"as":[20],"far-reaching":[22],"generalization":[23],"of":[24,33,36,41,63,111,120,136,146,172],"the":[25,31,53,61,118,121,133,137,143,170],"(well-studied)":[26],"classical":[27,105],"on":[30,52,60,76,149,162],"set":[32],"order":[34,50,145],"ideals":[35],"$P$.":[37],"Continuing":[38],"our":[39],"exploration":[40],"this":[42],"rowmotion,":[44,106],"we":[45,71],"prove":[46,132],"that":[47],"it":[48,84,96],"$p+q$":[51],"$\\left(":[54],"p,":[55],"q\\right)":[56],"$-rectangle":[57],"(i.e.,":[59],"product":[62],"$p$-element":[65],"chain":[66],"with":[67],"$q$-element":[69],"chain);":[70],"also":[72],"compute":[73],"its":[74],"orders":[75],"some":[77],"triangle-shaped":[78],"posets.":[79,174],"In":[80],"all":[81],"cases":[82],"mentioned,":[83],"turns":[85],"out":[86],"have":[88],"(and":[90],"explicitly":[91],"computable)":[92],"order,":[93],"property":[95],"does":[97],"not":[98],"exhibit":[99],"for":[100],"general":[101],"posets":[103,151],"(unlike":[104],"which":[107],"is":[108],"permutation":[110],"set).":[114],"Our":[115],"proof":[116],"in":[117,141],"case":[119,135],"rectangle":[122],"uses":[124],"an":[125,155],"idea":[126],"Volkov":[129],"(arXiv:hep-th/0606094)":[130],"$AA$":[134],"Zamolodchikov":[138,158],"periodicity":[139],"conjecture;":[140],"fact,":[142],"many":[150],"can":[152],"be":[153],"considered":[154],"analogue":[156],"periodicity.":[159],"We":[160],"comment":[161],"suspected,":[163],"but":[164],"so":[165],"far":[166],"enigmatic,":[167],"connections":[168],"theory":[171],"root":[173]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}