{"id":"https://openalex.org/W3043486073","doi":"https://doi.org/10.37236/9779","title":"Domino Tilings of Cylinders: Connected Components under Flips and Normal Distribution of the Twist","display_name":"Domino Tilings of Cylinders: Connected Components under Flips and Normal Distribution of the Twist","publication_year":2021,"publication_date":"2021-02-11","ids":{"openalex":"https://openalex.org/W3043486073","doi":"https://doi.org/10.37236/9779","mag":"3043486073"},"language":"en","primary_location":{"id":"doi:10.37236/9779","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9779","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p28/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":"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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p28/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091682509","display_name":"Nicolau C. Saldanha","orcid":"https://orcid.org/0000-0002-3953-5366"},"institutions":[{"id":"https://openalex.org/I2699952","display_name":"Pontifical Catholic University of Rio de Janeiro","ror":"https://ror.org/01dg47b60","country_code":"BR","type":"education","lineage":["https://openalex.org/I2699952"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Nicolau C. Saldanha","raw_affiliation_strings":["PUC-Rio"],"affiliations":[{"raw_affiliation_string":"PUC-Rio","institution_ids":["https://openalex.org/I2699952"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091682509"],"corresponding_institution_ids":["https://openalex.org/I2699952"],"apc_list":null,"apc_paid":null,"fwci":0.1594,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.3778345,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"28","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9915000200271606,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9879000186920166,"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/combinatorics","display_name":"Combinatorics","score":0.8179306983947754},{"id":"https://openalex.org/keywords/twist","display_name":"Twist","score":0.6577784419059753},{"id":"https://openalex.org/keywords/substitution-tiling","display_name":"Substitution tiling","score":0.6543906331062317},{"id":"https://openalex.org/keywords/domino","display_name":"Domino","score":0.6525826454162598},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.594014585018158},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.43572869896888733},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4326445460319519},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4199894070625305},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3456413149833679},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.30579674243927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18355873227119446}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8179306983947754},{"id":"https://openalex.org/C2776196297","wikidata":"https://www.wikidata.org/wiki/Q17138781","display_name":"Twist","level":2,"score":0.6577784419059753},{"id":"https://openalex.org/C21550011","wikidata":"https://www.wikidata.org/wiki/Q7632143","display_name":"Substitution tiling","level":2,"score":0.6543906331062317},{"id":"https://openalex.org/C2776416436","wikidata":"https://www.wikidata.org/wiki/Q3751781","display_name":"Domino","level":3,"score":0.6525826454162598},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.594014585018158},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.43572869896888733},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4326445460319519},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4199894070625305},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3456413149833679},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30579674243927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18355873227119446},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C161790260","wikidata":"https://www.wikidata.org/wiki/Q82264","display_name":"Catalysis","level":2,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/9779","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9779","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p28/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":"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:arXiv.org:2007.09500","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.09500","pdf_url":"https://arxiv.org/pdf/2007.09500","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3043486073","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2007.09500.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2007.09500","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2007.09500","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/9779","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9779","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p28/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":"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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3043486073.pdf","grobid_xml":"https://content.openalex.org/works/W3043486073.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1858129486","https://openalex.org/W1968989936","https://openalex.org/W1977661736","https://openalex.org/W2014904423","https://openalex.org/W2018696655","https://openalex.org/W2619215003","https://openalex.org/W2998668978","https://openalex.org/W3042344420","https://openalex.org/W3103373810","https://openalex.org/W6678024890"],"related_works":["https://openalex.org/W3133141451","https://openalex.org/W2998668978","https://openalex.org/W2060960097","https://openalex.org/W2333462270","https://openalex.org/W2222765766","https://openalex.org/W1560526706","https://openalex.org/W2083428119","https://openalex.org/W2794516517","https://openalex.org/W2951922588","https://openalex.org/W3095587871","https://openalex.org/W2950670972","https://openalex.org/W3173082064","https://openalex.org/W316859547","https://openalex.org/W1991507146","https://openalex.org/W1973439199","https://openalex.org/W2006474580","https://openalex.org/W104425819","https://openalex.org/W2010247425","https://openalex.org/W1510323778","https://openalex.org/W1996762867"],"abstract_inverted_index":{"We":[0,18,54],"consider":[1],"domino":[2,10,233,243],"tilings":[3,102,164,184,226,252],"of":[4,24,106,121,160,163,165,188,198,225,248,251,253],"$3$-dimensional":[5],"cubiculated":[6],"regions.":[7],"A":[8,68,93],"three-dimensional":[9],"is":[11,36,70,89,97,128,216],"a":[12,37,65,71,84,119,174,196,219,228],"$2\\times":[13],"1\\times":[14],"1$":[15],"rectangular":[16],"cuboid.":[17],"are":[19,78,133],"particularly":[20,261],"interested":[21],"in":[22,83],"regions":[23],"the":[25,44,62,154,161,166,179,223,231,239,242,249,254],"form":[26],"$\\mathcal{R}_N":[27,168,256],"=":[28,110,138,169,257],"\\mathcal{D}":[29,170,258],"\\times":[30,140,171,190,259],"[0,N]$":[31,191],"where":[32],"$\\mathcal{D}":[33,137,189],"\\subset":[34],"\\mathbb{R}^2$":[35],"fixed":[38],"quadriculated":[39,94],"disk.":[40],"In":[41],"dimension":[42],"$3$,":[43],"twist":[45,63,88],"associates":[46],"to":[47,60,201,209],"each":[48],"tiling":[49],"$\\mathbf{t}$":[50],"an":[51],"integer":[52],"$\\operatorname{Tw}(\\mathbf{t})$.":[53],"prove":[55],"that,":[56],"when":[57],"$N$":[58],"goes":[59],"infinity,":[61],"follows":[64],"normal":[66],"distribution.":[67],"flip":[69],"local":[72],"move:":[73],"two":[74,101,182],"neighboring":[75],"parallel":[76],"dominoes":[77],"removed":[79],"and":[80,104,113,145,186,212],"placed":[81],"back":[82],"different":[85],"position.":[86],"The":[87],"invariant":[90],"under":[91,158],"flips.":[92],"disk":[95],"$\\mathcal{D}$":[96,215],"regular":[98,150],"if,":[99],"whenever":[100],"$\\mathbf{t}_0$":[103,112],"$\\mathbf{t}_1$":[105,114],"$\\mathcal{R}_N$":[107],"satisfy":[108],"$\\operatorname{Tw}(\\mathbf{t}_0)":[109],"\\operatorname{Tw}(\\mathbf{t}_1)$,":[111],"can":[115,192],"be":[116,178,193],"joined":[117,194],"by":[118,195],"sequence":[120,197],"flips":[122,159,199],"provided":[123],"some":[124],"extra":[125],"vertical":[126],"space":[127,250],"allowed.":[129],"Many":[130],"large":[131,263],"disks":[132],"regular,":[134],"including":[135],"rectangles":[136],"[0,L]":[139],"[0,M]$":[141],"with":[142],"$LM$":[143],"even":[144],"$\\min\\{L,M\\}":[146],"\\ge":[147],"3$.":[148],"For":[149],"disks,":[151],"we":[152],"describe":[153],"larger":[155],"connected":[156],"components":[157],"set":[162,224],"region":[167],"[0,N]$.":[172],"As":[173],"corollary,":[175],"let":[176],"$p_N$":[177,207],"probability":[180],"that":[181,241],"random":[183],"$\\mathbf{T}_0$":[185],"$\\mathbf{T}_1$":[187],"conditional":[200],"their":[202],"twists":[203],"being":[204],"equal.":[205],"Then":[206],"tends":[208],"$1$":[210],"if":[211,214],"only":[213],"regular.":[217],"Under":[218],"suitable":[220],"equivalence":[221],"relation,":[222],"has":[227],"group":[229,244],"structure,":[230],"{\\em":[232],"group}":[234],"$G_{\\mathcal{D}}$.":[235],"These":[236],"results":[237],"illustrate":[238],"fact":[240],"dictates":[245],"many":[246],"properties":[247],"cylinder":[255],"[0,N]$,":[260],"for":[262],"$N$.":[264]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}