{"id":"https://openalex.org/W1503014997","doi":"https://doi.org/10.37236/1041","title":"Tilings by Translation: Enumeration by a Rational Language Approach","display_name":"Tilings by Translation: Enumeration by a Rational Language Approach","publication_year":2006,"publication_date":"2006-02-15","ids":{"openalex":"https://openalex.org/W1503014997","doi":"https://doi.org/10.37236/1041","mag":"1503014997"},"language":"en","primary_location":{"id":"doi:10.37236/1041","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1041","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r15/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/v13i1r15/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107234313","display_name":"Sre\u010dko Brlek","orcid":null},"institutions":[{"id":"https://openalex.org/I159129438","display_name":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","ror":"https://ror.org/002rjbv21","country_code":"CA","type":"education","lineage":["https://openalex.org/I159129438","https://openalex.org/I49663120"]},{"id":"https://openalex.org/I4210161954","display_name":"D\u00e9partement d'Informatique","ror":"https://ror.org/05y6rqs46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210159245","https://openalex.org/I4210161954"]}],"countries":["CA","FR"],"is_corresponding":false,"raw_author_name":"Srecko Brlek","raw_affiliation_strings":["Lab. Combinatoire et d'Informatique Mathmatique, Un. Qubec Montral, CP 8888 Succ. Centre-ville, Montral (QC) Canada H3C 3P8","Universite du Quebec `a Montreal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lab. Combinatoire et d'Informatique Mathmatique, Un. Qubec Montral, CP 8888 Succ. Centre-ville, Montral (QC) Canada H3C 3P8","institution_ids":["https://openalex.org/I4210161954"]},{"raw_affiliation_string":"Universite du Quebec `a Montreal","institution_ids":["https://openalex.org/I159129438"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008742130","display_name":"Andrea Frosini","orcid":"https://orcid.org/0000-0001-7210-2231"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Frosini","raw_affiliation_strings":["Dip. di Scienze Matematiche e Informatiche, Universit di Siena, Pian dei Mantellini 44, Siena, Italy","University of Siena ()"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dip. di Scienze Matematiche e Informatiche, Universit di Siena, Pian dei Mantellini 44, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"University of Siena ()","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018231504","display_name":"Simone Rinaldi","orcid":null},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Simone Rinaldi","raw_affiliation_strings":["Dip. di Scienze Matematiche e Informatiche, Universit di Siena, Pian dei Mantellini 44, Siena, Italy","University of Siena ()"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dip. di Scienze Matematiche e Informatiche, Universit di Siena, Pian dei Mantellini 44, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"University of Siena ()","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033058854","display_name":"Laurent Vuillon","orcid":"https://orcid.org/0000-0002-3707-659X"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I70900168","display_name":"Universit\u00e9 Savoie Mont Blanc","ror":"https://ror.org/04gqg1a07","country_code":"FR","type":"education","lineage":["https://openalex.org/I70900168"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Laurent Vuillon","raw_affiliation_strings":["Laboratoire de Mathmatiques,UMR 5127 CNRS, Universit de Savoie, 73376 Le Bourget du Lac, France,","University of Savoy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Mathmatiques,UMR 5127 CNRS, Universit de Savoie, 73376 Le Bourget du Lac, France,","institution_ids":["https://openalex.org/I70900168","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"University of Savoy","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9464,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.67705263,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"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":0.9997000098228455,"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":0.9997000098228455,"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/T12162","display_name":"Cellular Automata and Applications","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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9969000220298767,"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/polyomino","display_name":"Polyomino","score":0.990641713142395},{"id":"https://openalex.org/keywords/parallelogram","display_name":"Parallelogram","score":0.8243757486343384},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7863451242446899},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.7690292596817017},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7396015524864197},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5873482823371887},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5617788434028625},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5404714941978455},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5254817605018616},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.49127906560897827},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47477173805236816},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.44026806950569153},{"id":"https://openalex.org/keywords/combinatorics-on-words","display_name":"Combinatorics on words","score":0.4268278181552887},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40674853324890137},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.24396243691444397},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15279468894004822},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10707691311836243},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06770357489585876}],"concepts":[{"id":"https://openalex.org/C69919132","wikidata":"https://www.wikidata.org/wiki/Q1144819","display_name":"Polyomino","level":3,"score":0.990641713142395},{"id":"https://openalex.org/C53118041","wikidata":"https://www.wikidata.org/wiki/Q45867","display_name":"Parallelogram","level":3,"score":0.8243757486343384},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7863451242446899},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.7690292596817017},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7396015524864197},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5873482823371887},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5617788434028625},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5404714941978455},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5254817605018616},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.49127906560897827},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47477173805236816},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.44026806950569153},{"id":"https://openalex.org/C164804908","wikidata":"https://www.wikidata.org/wiki/Q2985058","display_name":"Combinatorics on words","level":3,"score":0.4268278181552887},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40674853324890137},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.24396243691444397},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15279468894004822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10707691311836243},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06770357489585876},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.0},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/1041","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1041","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r15/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.80.3252","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.80.3252","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lama.univ-savoie.fr/~vuillon/psp_final.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.92.6634","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.6634","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1r15.pdf","raw_type":"text"},{"id":"pmh:oai:usiena-air.unisi.it:11365/10579","is_oa":false,"landing_page_url":"http://hdl.handle.net/11365/10579","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:zenodo.org:125193","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/125193","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.37236/1041","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1041","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r15/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/W1503014997.pdf","grobid_xml":"https://content.openalex.org/works/W1503014997.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W35157995","https://openalex.org/W66519466","https://openalex.org/W135008847","https://openalex.org/W1514324498","https://openalex.org/W1518071186","https://openalex.org/W1537523458","https://openalex.org/W1551177513","https://openalex.org/W1796115931","https://openalex.org/W1980257749","https://openalex.org/W1980939657","https://openalex.org/W1986667059","https://openalex.org/W1997965066","https://openalex.org/W1999694873","https://openalex.org/W2013972736","https://openalex.org/W2017025480","https://openalex.org/W2036252950","https://openalex.org/W2038555168","https://openalex.org/W2043452116","https://openalex.org/W2049151402","https://openalex.org/W2069325427","https://openalex.org/W2081302100","https://openalex.org/W2082141815","https://openalex.org/W2111636325","https://openalex.org/W2126209209","https://openalex.org/W2157575511","https://openalex.org/W2327692812","https://openalex.org/W2914659449","https://openalex.org/W2949176902","https://openalex.org/W4239917935"],"related_works":["https://openalex.org/W4299575066","https://openalex.org/W2564134132","https://openalex.org/W2951308736","https://openalex.org/W2011263427","https://openalex.org/W6455561","https://openalex.org/W2054730479","https://openalex.org/W1537657985","https://openalex.org/W2563330252","https://openalex.org/W4236183709","https://openalex.org/W2405894551"],"abstract_inverted_index":{"Beauquier":[0],"and":[1,4,31],"Nivat":[2],"introduced":[3],"gave":[5],"a":[6,23,71,82],"characterization":[7,65],"of":[8,11,54,70,76,79,92],"the":[9,19,26,51,63,74,77,88],"class":[10],"pseudo-square":[12,55,93],"polyominoes,":[13],"i.e.":[14],"those":[15],"polyominoes":[16,56,95],"that":[17],"tile":[18],"plane":[20,27],"by":[21,28,68],"translation:":[22],"polyomino":[24],"tiles":[25],"translation":[29],"if":[30,33],"only":[32],"its":[34],"boundary":[35],"word":[36],"$W$":[37],"may":[38],"be":[39],"factorized":[40],"as":[41],"$W":[42],"=":[43],"XY\\overline{X}":[44],"\\,\\overline{Y}$.":[45],"In":[46],"this":[47],"paper":[48],"we":[49,66],"consider":[50],"subclass":[52,78],"PSP":[53],"which":[57],"are":[58],"also":[59,97],"parallelogram.":[60],"By":[61],"using":[62],"Beauquier-Nivat":[64],"provide":[67],"means":[69],"rational":[72],"language":[73],"enumeration":[75],"$psp$-polyominoes":[80],"with":[81],"fixed":[83],"planar":[84],"basis":[85],"according":[86],"to":[87],"semi-perimeter.":[89],"The":[90],"case":[91],"convex":[94],"is":[96],"analyzed.":[98]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
