{"id":"https://openalex.org/W4390103546","doi":"https://doi.org/10.5070/c63362790","title":"Birational rowmotion on a rectangle over a noncommutative ring","display_name":"Birational rowmotion on a rectangle over a noncommutative ring","publication_year":2023,"publication_date":"2023-12-22","ids":{"openalex":"https://openalex.org/W4390103546","doi":"https://doi.org/10.5070/c63362790"},"language":"en","primary_location":{"id":"doi:10.5070/c63362790","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c63362790","pdf_url":"https://escholarship.org/content/qt5407m0q4/qt5407m0q4.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt5407m0q4/qt5407m0q4.pdf","any_repository_has_fulltext":false},"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/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Darij Grinberg","raw_affiliation_strings":["Department of Mathematics, Drexel University, Philadelphia, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Drexel University, Philadelphia, U.S.A","institution_ids":["https://openalex.org/I72816309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071443532","display_name":"Tom Roby","orcid":null},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tom Roby","raw_affiliation_strings":["University of Connecticut, Connecticut, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Connecticut, Connecticut, U.S.A","institution_ids":["https://openalex.org/I140172145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31022992,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"3","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":0.9994999766349792,"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":0.9994999766349792,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9993000030517578,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.816107988357544},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.7756403088569641},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7389035224914551},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7216010689735413},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6458368301391602},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5504640936851501},{"id":"https://openalex.org/keywords/cluster-algebra","display_name":"Cluster algebra","score":0.5290985107421875},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5187302231788635},{"id":"https://openalex.org/keywords/star-product","display_name":"Star product","score":0.4468404948711395},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.42702940106391907},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3750828206539154},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2537425458431244},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10122504830360413}],"concepts":[{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.816107988357544},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.7756403088569641},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7389035224914551},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7216010689735413},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6458368301391602},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5504640936851501},{"id":"https://openalex.org/C165879259","wikidata":"https://www.wikidata.org/wiki/Q5136690","display_name":"Cluster algebra","level":3,"score":0.5290985107421875},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5187302231788635},{"id":"https://openalex.org/C195800304","wikidata":"https://www.wikidata.org/wiki/Q7601281","display_name":"Star product","level":2,"score":0.4468404948711395},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.42702940106391907},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3750828206539154},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2537425458431244},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10122504830360413},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5070/c63362790","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c63362790","pdf_url":"https://escholarship.org/content/qt5407m0q4/qt5407m0q4.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.5070/c63362790","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c63362790","pdf_url":"https://escholarship.org/content/qt5407m0q4/qt5407m0q4.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320328470","display_name":"Mathematisches Forschungsinstitut Oberwolfach","ror":"https://ror.org/001zbj766"},{"id":"https://openalex.org/F4320329205","display_name":"Banff International Research Station for Mathematical Innovation and Discovery","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390103546.pdf","grobid_xml":"https://content.openalex.org/works/W4390103546.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1490068203","https://openalex.org/W1554619904","https://openalex.org/W1837322850","https://openalex.org/W1979423085","https://openalex.org/W2006159741","https://openalex.org/W2010142964","https://openalex.org/W2027275704","https://openalex.org/W2095420391","https://openalex.org/W2108773821","https://openalex.org/W2128103201","https://openalex.org/W2283577362","https://openalex.org/W2463036700","https://openalex.org/W2557458073","https://openalex.org/W2595764319","https://openalex.org/W2962913694","https://openalex.org/W2963437007","https://openalex.org/W2993707243","https://openalex.org/W3006502557","https://openalex.org/W3080815705","https://openalex.org/W3102083284","https://openalex.org/W3103043466","https://openalex.org/W3103723015","https://openalex.org/W3155867610","https://openalex.org/W3187521469","https://openalex.org/W3193798259","https://openalex.org/W4206059043","https://openalex.org/W4213091363","https://openalex.org/W4224329318","https://openalex.org/W4287026932","https://openalex.org/W4292116637","https://openalex.org/W4300302225"],"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/W2789323833","https://openalex.org/W1975173901","https://openalex.org/W2024183080","https://openalex.org/W2951746344","https://openalex.org/W61453168"],"abstract_inverted_index":{"We":[0,255],"extend":[1,161],"the":[2,11,14,71,109,124,129,137,147,163,170,185,201,204,238,266,287,302,323,349],"periodicity":[3,208,248,261,290,300,313,347],"of":[4,44,55,103,131,139,142,149,153,207,220,268,291,345],"birational":[5,164,171,186,210,292,329],"rowmotion":[6,80,126,211,293,330],"for":[7,70,96,209,223,262,309],"rectangular":[8,213],"posets":[9,214],"to":[10,146,162,180,275,297,332,348],"case":[12],"when":[13],"base":[15],"field":[16],"is":[17,39,81,217],"replaced":[18],"by":[19,49,92,281],"a":[20,28,35,45,56,82,99,106,218,225,250,342],"noncommutative":[21,239,247,310,328,350,358],"ring":[22,57],"(under":[23],"appropriate":[24],"conditions).":[25],"This":[26],"resolves":[27],"conjecture":[29],"from":[30],"2014.":[31],"The":[32,119],"proof":[33,206],"uses":[34],"novel":[36],"approach":[37],"and":[38,66,74,94,190,227,249,265,283,306],"fully":[40],"self-contained.":[41],"Consider":[42],"labelings":[43],"finite":[46],"poset":[47,64],"\\(P\\)":[48,216],"\\(\\left\\vert":[50],"P\\right\\vert":[51],"+":[52],"2\\)":[53],"elements":[54,76],"\\(\\mathbb{K}\\):":[58],"one":[59],"label":[60],"associated":[61],"with":[62,257],"each":[63],"element":[65],"two":[67,221],"constant":[68],"labels":[69],"added":[72],"top":[73],"bottom":[75],"in":[77,121,194,237,286,301,316],"\\(\\widehat{P}\\).":[78],"Birational":[79],"partial":[83],"map":[84,107,127],"on":[85,108,128,212],"such":[86],"labelings.":[87],"It":[88],"was":[89],"originally":[90],"defined":[91],"Einstein":[93],"Propp":[95],"\\(\\mathbb{K}=\\mathbb{R}\\)":[97],"as":[98,341],"lifting":[100],"(via":[101],"detropicalization)":[102],"piecewise-linear":[104],"rowmotion,":[105],"order":[110,132,140,322],"polytope":[111],"\\(\\mathcal{O}(P)":[112],":=":[113],"\\{\\text{order-preserving":[114],"}":[115],"f:":[116],"P":[117],"\\to[0,1]\\}\\).":[118],"latter,":[120],"turn,":[122],"extends":[123],"well-studied":[125],"set":[130,138],"ideals":[133],"(or":[134],"more":[135],"properly,":[136],"filters)":[141],"\\(P\\),":[143],"which":[144],"correspond":[145],"vertices":[148],"\\(\\mathcal{O}(P)\\).":[150],"Dynamical":[151],"properties":[152,192],"these":[154],"combinatorial":[155,176],"maps":[156],"sometimes":[157],"(but":[158],"not":[159],"always)":[160],"level,":[165],"while":[166,327],"results":[167,271],"proven":[168],"at":[169,197],"level":[172,187],"always":[173],"imply":[174],"their":[175],"counterparts.":[177],"Allowing":[178],"\\(\\mathbb{K}\\)":[179,224],"be":[181,273,295,339],"noncommutative,":[182],"we":[183,244],"generalize":[184],"even":[188,315],"further,":[189],"some":[191,258],"are":[193,325],"fact":[195],"lost":[196],"this":[198,242,246],"step.In":[199],"2014,":[200],"authors":[202],"gave":[203],"first":[205],"(when":[215],"product":[219],"chains)":[222],"field,":[226],"conjectured":[228],"that":[229],"it":[230],"survives":[231],"(in":[232],"an":[233],"appropriately":[234],"twisted":[235],"form)":[236],"case.":[240],"In":[241],"paper,":[243],"prove":[245],"concomitant":[251],"antipodal":[252],"reciprocity":[253],"formula.":[254],"end":[256],"conjectures":[259],"about":[260],"other":[263],"posets,":[264,357,368],"question":[267],"whether":[269],"our":[270,336],"can":[272,294,338],"extended":[274],"(noncommutative)":[276],"semirings.It":[277],"has":[278],"been":[279],"observed":[280],"Glick":[282],"Grinberg":[284],"that,":[285],"commutative":[288],"case,":[289,305],"used":[296],"derive":[298],"Zamolodchikov":[299,312,346,361],"type":[303],"\\(AA\\)":[304],"vice-versa.":[307],"However,":[308],"\\(\\mathbb{K}\\),":[311],"fails":[314],"small":[317],"examples":[318],"(no":[319],"matter":[320],"what":[321],"factors":[324],"multiplied),":[326],"continues":[331],"exhibit":[333],"periodicity.":[334],"Thus,":[335],"result":[337],"viewed":[340],"lateral":[343],"generalization":[344],"setting.Mathematics":[351],"Subject":[352],"Classifications:":[353],"06A07,":[354],"05E99Keywords:":[355],"Rowmotion,":[356],"rings,":[359],"semirings,":[360],"periodicity,":[362],"root":[363],"systems,":[364],"promotion,":[365],"trees,":[366],"graded":[367],"Grassmannian,":[369],"tropicalization":[370]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}