{"id":"https://openalex.org/W4393318214","doi":"https://doi.org/10.1080/00029890.2024.2325863","title":"Following in Yiu\u2019s Footsteps but on the Eisenstein Lattice","display_name":"Following in Yiu\u2019s Footsteps but on the Eisenstein Lattice","publication_year":2024,"publication_date":"2024-03-29","ids":{"openalex":"https://openalex.org/W4393318214","doi":"https://doi.org/10.1080/00029890.2024.2325863"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2024.2325863","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2024.2325863","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004130284","display_name":"Christian Aebi","orcid":"https://orcid.org/0000-0002-8667-5214"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christian Aebi","raw_affiliation_strings":["Coll\u00e8ge Calvin, Geneva, Switzerland 1211"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Coll\u00e8ge Calvin, Geneva, Switzerland 1211","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032893071","display_name":"Grant Cairns","orcid":"https://orcid.org/0000-0002-9011-4567"},"institutions":[{"id":"https://openalex.org/I196829312","display_name":"La Trobe University","ror":"https://ror.org/01rxfrp27","country_code":"AU","type":"education","lineage":["https://openalex.org/I196829312"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Grant Cairns","raw_affiliation_strings":["Department of Mathematical and Physical Sciences, La Trobe University, Melbourne, Australia 3086"],"raw_orcid":"https://orcid.org/0000-0002-9011-4567","affiliations":[{"raw_affiliation_string":"Department of Mathematical and Physical Sciences, La Trobe University, Melbourne, Australia 3086","institution_ids":["https://openalex.org/I196829312"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004130284"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9603,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.74982662,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"131","issue":"6","first_page":"526","last_page":"529"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.34689998626708984,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.34689998626708984,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4883856177330017},{"id":"https://openalex.org/keywords/art","display_name":"Art","score":0.33846157789230347},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27179044485092163},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.20564153790473938}],"concepts":[{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4883856177330017},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.33846157789230347},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27179044485092163},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.20564153790473938}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2024.2325863","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2024.2325863","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W598164486","https://openalex.org/W2018760182","https://openalex.org/W4210774655","https://openalex.org/W4233185505","https://openalex.org/W4255749072","https://openalex.org/W4256259790","https://openalex.org/W7038710964"],"related_works":["https://openalex.org/W4387497383","https://openalex.org/W3183948672","https://openalex.org/W3173606202","https://openalex.org/W3110381201","https://openalex.org/W2948807893","https://openalex.org/W2935909890","https://openalex.org/W2778153218","https://openalex.org/W2758277628","https://openalex.org/W2748952813","https://openalex.org/W1531601525"],"abstract_inverted_index":{"Paul":[0],"Yiu":[1],"proved":[2],"that":[3],"all":[4],"Heron":[5],"triangles":[6,19],"are":[7],"realizable":[8],"on":[9,22],"the":[10,23],"integer":[11],"lattice.":[12,25],"We":[13],"give":[14],"an":[15],"analogous":[16],"result":[17],"for":[18],"with":[20],"vertices":[21],"Eisenstein":[24]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}