{"id":"https://openalex.org/W1985005004","doi":"https://doi.org/10.1007/s00454-012-9433-5","title":"Minkowski Length of 3D Lattice Polytopes","display_name":"Minkowski Length of 3D Lattice Polytopes","publication_year":2012,"publication_date":"2012-06-27","ids":{"openalex":"https://openalex.org/W1985005004","doi":"https://doi.org/10.1007/s00454-012-9433-5","mag":"1985005004"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-012-9433-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9433-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9433-5.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9433-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046893825","display_name":"Olivia Beckwith","orcid":"https://orcid.org/0000-0002-5547-8592"},"institutions":[{"id":"https://openalex.org/I133543626","display_name":"Harvey Mudd College","ror":"https://ror.org/025ecfn45","country_code":"US","type":"education","lineage":["https://openalex.org/I133543626"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Olivia Beckwith","raw_affiliation_strings":["Harvey Mudd College"],"affiliations":[{"raw_affiliation_string":"Harvey Mudd College","institution_ids":["https://openalex.org/I133543626"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044814529","display_name":"Matthew Grimm","orcid":null},"institutions":[{"id":"https://openalex.org/I4210140792","display_name":"Universidad Cat\u00f3lica Santo Domingo","ror":"https://ror.org/04ytq6y86","country_code":"DO","type":"education","lineage":["https://openalex.org/I4210140792"]}],"countries":["DO"],"is_corresponding":false,"raw_author_name":"Matthew Grimm","raw_affiliation_strings":["UCSD;"],"affiliations":[{"raw_affiliation_string":"UCSD;","institution_ids":["https://openalex.org/I4210140792"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008244060","display_name":"Jenya Soprunova","orcid":"https://orcid.org/0000-0003-0172-2948"},"institutions":[{"id":"https://openalex.org/I149910238","display_name":"Kent State University","ror":"https://ror.org/049pfb863","country_code":"US","type":"education","lineage":["https://openalex.org/I149910238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jenya Soprunova","raw_affiliation_strings":["Kent State Univ"],"affiliations":[{"raw_affiliation_string":"Kent State Univ","institution_ids":["https://openalex.org/I149910238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071987223","display_name":"Bradley Weaver","orcid":null},"institutions":[{"id":"https://openalex.org/I181598100","display_name":"Grove City College","ror":"https://ror.org/01755xe07","country_code":"US","type":"education","lineage":["https://openalex.org/I181598100"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bradley Weaver","raw_affiliation_strings":["Grove City College#TAB#"],"affiliations":[{"raw_affiliation_string":"Grove City College#TAB#","institution_ids":["https://openalex.org/I181598100"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5046893825"],"corresponding_institution_ids":["https://openalex.org/I133543626"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.0493,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75507678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9980000257492065,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9955999851226807,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.9154764413833618},{"id":"https://openalex.org/keywords/minkowski-addition","display_name":"Minkowski addition","score":0.8803771734237671},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.8272631764411926},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.752951979637146},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.7086297869682312},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.665790319442749},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.6082048416137695},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.544283390045166},{"id":"https://openalex.org/keywords/minkowskis-theorem","display_name":"Minkowski's theorem","score":0.47287625074386597},{"id":"https://openalex.org/keywords/geometry-of-numbers","display_name":"Geometry of numbers","score":0.4340784549713135},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21461474895477295},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17278847098350525},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10620442032814026}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9154764413833618},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.8803771734237671},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.8272631764411926},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.752951979637146},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.7086297869682312},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.665790319442749},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6082048416137695},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.544283390045166},{"id":"https://openalex.org/C79013991","wikidata":"https://www.wikidata.org/wiki/Q1097021","display_name":"Minkowski's theorem","level":3,"score":0.47287625074386597},{"id":"https://openalex.org/C73038302","wikidata":"https://www.wikidata.org/wiki/Q1466519","display_name":"Geometry of numbers","level":3,"score":0.4340784549713135},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21461474895477295},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17278847098350525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10620442032814026},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00454-012-9433-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9433-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9433-5.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1202.0524","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1202.0524","pdf_url":"https://arxiv.org/pdf/1202.0524","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.363.6359","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.363.6359","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.kent.edu/~soprunova/pdf/mink_length.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.569.4802","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.569.4802","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.kent.edu/~soprunova/pdf/mink_length.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.751.8253","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.751.8253","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1202.0524.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-012-9433-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9433-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9433-5.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1156100412","display_name":"REU Site at Kent State University: Applications and Ramifications of Linear Algebra","funder_award_id":"0755318","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1985005004.pdf","grobid_xml":"https://content.openalex.org/works/W1985005004.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1964542422","https://openalex.org/W2056558741","https://openalex.org/W2078768576","https://openalex.org/W2092348813","https://openalex.org/W2105352202","https://openalex.org/W2129740858","https://openalex.org/W2160273855","https://openalex.org/W2180062674","https://openalex.org/W2233474732","https://openalex.org/W3195834405","https://openalex.org/W4292929315"],"related_works":["https://openalex.org/W960999769","https://openalex.org/W3124338670","https://openalex.org/W4211088175","https://openalex.org/W3037418146","https://openalex.org/W2950428426","https://openalex.org/W4309277470","https://openalex.org/W3212521755","https://openalex.org/W4226494357","https://openalex.org/W2045562233","https://openalex.org/W2953253273"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}