{"id":"https://openalex.org/W4399325992","doi":"https://doi.org/10.1007/s00454-024-00659-5","title":"Classification of Width 1 Lattice Tetrahedra by Their Multi-Width","display_name":"Classification of Width 1 Lattice Tetrahedra by Their Multi-Width","publication_year":2024,"publication_date":"2024-06-04","ids":{"openalex":"https://openalex.org/W4399325992","doi":"https://doi.org/10.1007/s00454-024-00659-5"},"language":"lv","primary_location":{"id":"doi:10.1007/s00454-024-00659-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-024-00659-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-024-00659-5.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/s00454-024-00659-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032431445","display_name":"Girtrude Hamm","orcid":"https://orcid.org/0009-0001-2097-3294"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Girtrude Hamm","raw_affiliation_strings":["Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK"],"raw_orcid":"https://orcid.org/0009-0001-2097-3294","affiliations":[{"raw_affiliation_string":"Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK","institution_ids":["https://openalex.org/I142263535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032431445"],"corresponding_institution_ids":["https://openalex.org/I142263535"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.044148,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"73","issue":"3","first_page":"859","last_page":"885"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9879000186920166,"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":0.9879000186920166,"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":0.9860000014305115,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.983299970626831,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.7291381359100342},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5596790313720703},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.5376279354095459},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.3704771399497986},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.3025311231613159},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17794668674468994},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.13783949613571167}],"concepts":[{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.7291381359100342},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5596790313720703},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.5376279354095459},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.3704771399497986},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.3025311231613159},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17794668674468994},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.13783949613571167},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-024-00659-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-024-00659-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-024-00659-5.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"},{"id":"pmh:oai:nottingham-repository.worktribe.com:35730708","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/35730708","pdf_url":"https://nottingham-repository.worktribe.com/file/35730708/1/s00454-024-00659-5","source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"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":"publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s00454-024-00659-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-024-00659-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-024-00659-5.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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399325992.pdf"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1964542422","https://openalex.org/W1999004187","https://openalex.org/W2021567595","https://openalex.org/W2334989808","https://openalex.org/W2883073730","https://openalex.org/W3038801735","https://openalex.org/W4237930986","https://openalex.org/W4393894151"],"related_works":["https://openalex.org/W3118783749","https://openalex.org/W2002583644","https://openalex.org/W3119989344","https://openalex.org/W2025402442","https://openalex.org/W2098990162","https://openalex.org/W2993813190","https://openalex.org/W2567351266","https://openalex.org/W2378541949","https://openalex.org/W1030387743","https://openalex.org/W4363672148"],"abstract_inverted_index":{"Abstract":[0],"We":[1,62],"introduce":[2],"the":[3,112],"multi-width":[4,20,69],"of":[5,58,117],"a":[6,51],"lattice":[7,17,56,115],"polytope":[8],"and":[9,14,99,108],"use":[10,63],"this":[11,45,64],"to":[12,54,65],"classify":[13,55,66],"count":[15],"all":[16],"tetrahedra":[18,57,67,116],"with":[19,68],"$$(1,w_2,w_3)$$":[21],"<mml:math":[22,71,92,101],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[23,72,93,102],"<mml:mrow>":[24,73],"<mml:mo>(</mml:mo>":[25,74],"<mml:mn>1</mml:mn>":[26],"<mml:mo>,</mml:mo>":[27,32,76,81],"<mml:msub>":[28,33,77,82,94,103],"<mml:mi>w</mml:mi>":[29,34,78,83,95,104],"<mml:mn>2</mml:mn>":[30,75,79,96],"</mml:msub>":[31,36,80,85,97,106],"<mml:mn>3</mml:mn>":[35,84,105],"<mml:mo>)</mml:mo>":[37,86],"</mml:mrow>":[38,87],"</mml:math>":[39,88,98,107],".":[40],"The":[41],"approach":[42],"used":[43],"in":[44],"classification":[46],"can":[47],"be":[48],"extended":[49],"into":[50],"computer":[52],"algorithm":[53],"any":[59,118],"given":[60],"multi-width.":[61,119],"$$(2,w_2,w_3)$$":[70],"for":[89],"small":[90],"$$w_2$$":[91],"$$w_3$$":[100],"make":[109],"conjectures":[110],"about":[111],"function":[113],"counting":[114]},"counts_by_year":[],"updated_date":"2025-12-28T23:10:05.387466","created_date":"2025-10-10T00:00:00"}