{"id":"https://openalex.org/W2892317171","doi":"https://doi.org/10.3390/sym10100511","title":"Cut-and-Project Schemes for Pisot Family Substitution Tilings","display_name":"Cut-and-Project Schemes for Pisot Family Substitution Tilings","publication_year":2018,"publication_date":"2018-10-16","ids":{"openalex":"https://openalex.org/W2892317171","doi":"https://doi.org/10.3390/sym10100511","mag":"2892317171"},"language":"en","primary_location":{"id":"doi:10.3390/sym10100511","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10100511","pdf_url":"https://www.mdpi.com/2073-8994/10/10/511/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/10/10/511/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078860848","display_name":"Jeong-Yup Lee","orcid":"https://orcid.org/0000-0002-3587-0992"},"institutions":[{"id":"https://openalex.org/I89079967","display_name":"Catholic Kwandong University","ror":"https://ror.org/05n486907","country_code":"KR","type":"education","lineage":["https://openalex.org/I89079967"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Jeong-Yup Lee","raw_affiliation_strings":["Department of Mathematics Education, Catholic Kwandong University, Gangneung, Gangwon 210-701, Korea, or KIAS, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, Korea"],"raw_orcid":"https://orcid.org/0000-0002-3587-0992","affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Catholic Kwandong University, Gangneung, Gangwon 210-701, Korea, or KIAS, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, Korea","institution_ids":["https://openalex.org/I89079967"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067137356","display_name":"Shigeki Akiyama","orcid":"https://orcid.org/0000-0001-7549-6686"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shigeki Akiyama","raw_affiliation_strings":["Institute of Mathematics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, Japan"],"raw_orcid":"https://orcid.org/0000-0001-7549-6686","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007657641","display_name":"Yasushi Nagai","orcid":"https://orcid.org/0000-0002-3773-6789"},"institutions":[{"id":"https://openalex.org/I182712176","display_name":"Montanuniversit\u00e4t Leoben","ror":"https://ror.org/02fhfw393","country_code":"AT","type":"education","lineage":["https://openalex.org/I182712176"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Yasushi Nagai","raw_affiliation_strings":["Lehrstuhl f\u00fcr Mathematik und Statistik, Department Mathematik und Informationstechnologie, Montanuniversit\u00e4t, Franz Josef Strasse 18, A-8700 Leoben, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehrstuhl f\u00fcr Mathematik und Statistik, Department Mathematik und Informationstechnologie, Montanuniversit\u00e4t, Franz Josef Strasse 18, A-8700 Leoben, Austria","institution_ids":["https://openalex.org/I182712176"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078860848"],"corresponding_institution_ids":["https://openalex.org/I89079967"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.4275,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6626249,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"10","issue":"10","first_page":"511","last_page":"511"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9987000226974487,"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9921000003814697,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9890000224113464,"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/substitution","display_name":"Substitution (logic)","score":0.7929965257644653},{"id":"https://openalex.org/keywords/unimodular-matrix","display_name":"Unimodular matrix","score":0.7679288983345032},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7475090026855469},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6163291335105896},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5634956955909729},{"id":"https://openalex.org/keywords/substitution-tiling","display_name":"Substitution tiling","score":0.5432485342025757},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5322971343994141},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.5249711871147156},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4520093500614166},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3631763160228729},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11629822850227356},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06858205795288086},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.060060709714889526}],"concepts":[{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.7929965257644653},{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.7679288983345032},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7475090026855469},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6163291335105896},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5634956955909729},{"id":"https://openalex.org/C21550011","wikidata":"https://www.wikidata.org/wiki/Q7632143","display_name":"Substitution tiling","level":2,"score":0.5432485342025757},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5322971343994141},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5249711871147156},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4520093500614166},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3631763160228729},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11629822850227356},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06858205795288086},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.060060709714889526},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym10100511","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10100511","pdf_url":"https://www.mdpi.com/2073-8994/10/10/511/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:bd8de2b45fcb4c15a1b8b0a29a2de45c","is_oa":true,"landing_page_url":"https://doaj.org/article/bd8de2b45fcb4c15a1b8b0a29a2de45c","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 10, Iss 10, p 511 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/10/10/511/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym10100511","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"},{"id":"pmh:oai:tsukuba.repo.nii.ac.jp:00052182","is_oa":true,"landing_page_url":"http://hdl.handle.net/2241/00157610","pdf_url":null,"source":{"id":"https://openalex.org/S4306402076","display_name":"Terrestrial Environment Research Center (University of Tsukuba)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I146399215","host_organization_name":"University of Tsukuba","host_organization_lineage":["https://openalex.org/I146399215"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.3390/sym10100511","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10100511","pdf_url":"https://www.mdpi.com/2073-8994/10/10/511/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G3267238357","display_name":null,"funder_award_id":"17K05159, 17H02849, BBD30028","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7852789520","display_name":null,"funder_award_id":"2017078374","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2892317171.pdf","grobid_xml":"https://content.openalex.org/works/W2892317171.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W95991007","https://openalex.org/W590026092","https://openalex.org/W1554576426","https://openalex.org/W1985563250","https://openalex.org/W1988277213","https://openalex.org/W2005714434","https://openalex.org/W2006018499","https://openalex.org/W2011201107","https://openalex.org/W2048945586","https://openalex.org/W2063558317","https://openalex.org/W2091510861","https://openalex.org/W2312324557","https://openalex.org/W2498026024","https://openalex.org/W2609357768","https://openalex.org/W2962718056","https://openalex.org/W2962767164","https://openalex.org/W3101417884","https://openalex.org/W3204164517","https://openalex.org/W4301022050","https://openalex.org/W4302606928","https://openalex.org/W6651946227","https://openalex.org/W6666258365"],"related_works":["https://openalex.org/W2011745869","https://openalex.org/W2088028898","https://openalex.org/W1974942973","https://openalex.org/W211627054","https://openalex.org/W1608437562","https://openalex.org/W2083668208","https://openalex.org/W3141916192","https://openalex.org/W2008654968","https://openalex.org/W2227321584","https://openalex.org/W4394645230"],"abstract_inverted_index":{"We":[0],"consider":[1],"Pisot":[2,27,56,108],"family":[3,28,57],"substitution":[4,110],"tilings":[5],"in":[6,112],"R":[7,45,113],"d":[8],"whose":[9],"dynamical":[10],"spectrum":[11],"is":[12,69,84],"pure":[13,35,79],"point.":[14],"There":[15],"are":[16,91],"two":[17,89,105,116],"cut-and-project":[18],"schemes":[19],"(CPSs)":[20],"which":[21],"arise":[22],"naturally:":[23],"one":[24],"from":[25,33,54,74],"the":[26,31,34,55,60,75,78,104,115,125],"property":[29],"and":[30,59],"other":[32],"point":[36,80],"spectrum.":[37,81],"The":[38],"first":[39],"CPS":[40,62],"has":[41,63],"an":[42,64,70],"internal":[43,65],"space":[44,66,72],"m":[46,50],"for":[47],"some":[48],"integer":[49],"\u2208":[51],"N":[52],"defined":[53,73],"property,":[58],"second":[61],"H":[67],"that":[68],"abstract":[71],"condition":[76,98],"of":[77],"However,":[82],"it":[83],"not":[85],"known":[86],"how":[87],"these":[88],"CPSs":[90,117],"related.":[92],"Here":[93],"we":[94],"provide":[95],"a":[96,101],"sufficient":[97],"to":[99,120,124],"make":[100],"connection":[102],"between":[103],"CPSs.":[106],"For":[107],"unimodular":[109],"tiling":[111],",":[114],"turn":[118],"out":[119],"be":[121],"same":[122],"due":[123],"remark":[126],"by":[127],"Barge-Kwapisz.":[128]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
