{"id":"https://openalex.org/W4407363329","doi":"https://doi.org/10.1007/s00454-025-00717-6","title":"An Alternative Proof for an Aperiodic Monotile","display_name":"An Alternative Proof for an Aperiodic Monotile","publication_year":2025,"publication_date":"2025-02-11","ids":{"openalex":"https://openalex.org/W4407363329","doi":"https://doi.org/10.1007/s00454-025-00717-6"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-025-00717-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00717-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00717-6.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00717-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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":true,"raw_author_name":"Shigeki Akiyama","raw_affiliation_strings":["Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, Japan"],"raw_orcid":"https://orcid.org/0000-0001-7549-6686","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050906949","display_name":"Yoshiaki Araki","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092990","display_name":"Tessella (United Kingdom)","ror":"https://ror.org/00fpcwp04","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210092990"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yoshiaki Araki","raw_affiliation_strings":["Japan Tessellation Design Association, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Japan Tessellation Design Association, Tokyo, Japan","institution_ids":["https://openalex.org/I4210092990"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067137356"],"corresponding_institution_ids":["https://openalex.org/I146399215"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":2.6514,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.88767368,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9970999956130981,"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":0.9970999956130981,"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/T12504","display_name":"Mathematics and Applications","score":0.9950000047683716,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/aperiodic-graph","display_name":"Aperiodic graph","score":0.8844751119613647},{"id":"https://openalex.org/keywords/proof-of-concept","display_name":"Proof of concept","score":0.4530208110809326},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4450153112411499},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3381533622741699},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3271709978580475},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12061750888824463},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.08364343643188477}],"concepts":[{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.8844751119613647},{"id":"https://openalex.org/C124978682","wikidata":"https://www.wikidata.org/wiki/Q1201019","display_name":"Proof of concept","level":2,"score":0.4530208110809326},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4450153112411499},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3381533622741699},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3271709978580475},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12061750888824463},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.08364343643188477}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-025-00717-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00717-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00717-6.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-025-00717-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00717-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00717-6.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7620049968","display_name":null,"funder_award_id":"20K03528","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"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/W4407363329.pdf","grobid_xml":"https://content.openalex.org/works/W4407363329.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W18182665","https://openalex.org/W584208200","https://openalex.org/W590026092","https://openalex.org/W1586417893","https://openalex.org/W1997759165","https://openalex.org/W2043318682","https://openalex.org/W2912420824","https://openalex.org/W2963429204","https://openalex.org/W2963943941","https://openalex.org/W3028224383","https://openalex.org/W4400197544","https://openalex.org/W6601163776"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W2037661079","https://openalex.org/W2339191433","https://openalex.org/W4287817191","https://openalex.org/W4298800952","https://openalex.org/W2039582600","https://openalex.org/W1992569127","https://openalex.org/W172284633"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"give":[2],"a":[3],"simple":[4],"alternative":[5],"proof":[6],"that":[7],"the":[8],"monotile":[9],"introduced":[10],"by":[11],"[14]":[12],"is":[13],"aperiodic.":[14]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-03-13T14:20:09.374765","created_date":"2025-10-10T00:00:00"}
