{"id":"https://openalex.org/W2036271623","doi":"https://doi.org/10.1007/pl00009415","title":"A Normal (0, 1)-Polytope None of Whose Regular Triangulations Is Unimodular","display_name":"A Normal (0, 1)-Polytope None of Whose Regular Triangulations Is Unimodular","publication_year":1999,"publication_date":"1999-02-01","ids":{"openalex":"https://openalex.org/W2036271623","doi":"https://doi.org/10.1007/pl00009415","mag":"2036271623"},"language":"en","primary_location":{"id":"doi:10.1007/pl00009415","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009415","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009415.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 &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/PL00009415.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046851808","display_name":"Hidefumi Ohsugi","orcid":"https://orcid.org/0000-0002-6403-1119"},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"Osaka University","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"H. Ohsugi","raw_affiliation_strings":["Department of Mathematics,  Graduate School of Science,  Osaka University,  Toyonaka, Osaka 560, Japan  smv067oh@ex.ecip.osaka-u.ac.jp  , , , , , , JP","Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan smv067oh@ex.ecip.osaka-u.ac.jp , JP"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics,  Graduate School of Science,  Osaka University,  Toyonaka, Osaka 560, Japan  smv067oh@ex.ecip.osaka-u.ac.jp  , , , , , , JP","institution_ids":["https://openalex.org/I98285908"]},{"raw_affiliation_string":"Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan smv067oh@ex.ecip.osaka-u.ac.jp , JP","institution_ids":["https://openalex.org/I98285908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005668319","display_name":"Takayuki Hibi","orcid":"https://orcid.org/0000-0002-7619-1152"},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"Osaka University","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]},{"id":"https://openalex.org/I14314212","display_name":"Osaka University of Economics","ror":"https://ror.org/04g11bp59","country_code":"JP","type":"education","lineage":["https://openalex.org/I14314212"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"T. Hibi","raw_affiliation_strings":["Department of Mathematics,  Graduate School of Science,  Osaka University,  Toyonaka, Osaka 560, Japan  hibi@math.sci.osaka-u.ac.jp, , , , , , JP","Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan hibi@math.sci.osaka-u.ac.jp, JP"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics,  Graduate School of Science,  Osaka University,  Toyonaka, Osaka 560, Japan  hibi@math.sci.osaka-u.ac.jp, , , , , , JP","institution_ids":["https://openalex.org/I98285908","https://openalex.org/I14314212"]},{"raw_affiliation_string":"Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan hibi@math.sci.osaka-u.ac.jp, JP","institution_ids":["https://openalex.org/I98285908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046851808"],"corresponding_institution_ids":["https://openalex.org/I98285908"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":3.7272,"has_fulltext":true,"cited_by_count":29,"citation_normalized_percentile":{"value":0.93393665,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"21","issue":"2","first_page":"201","last_page":"204"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9951000213623047,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/unimodular-matrix","display_name":"Unimodular matrix","score":0.9651930332183838},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8428652286529541},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8270249366760254},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7713530659675598},{"id":"https://openalex.org/keywords/uniform-k-21-polytope","display_name":"Uniform k 21 polytope","score":0.5031828284263611},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17971861362457275},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.1110943853855133}],"concepts":[{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.9651930332183838},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8428652286529541},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8270249366760254},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7713530659675598},{"id":"https://openalex.org/C16507315","wikidata":"https://www.wikidata.org/wiki/Q7885104","display_name":"Uniform k 21 polytope","level":5,"score":0.5031828284263611},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17971861362457275},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.1110943853855133},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.0},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/pl00009415","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009415","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009415.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 &amp; Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/pl00009415","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009415","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009415.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 &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G841385469","display_name":null,"funder_award_id":"9022140","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2036271623.pdf","grobid_xml":"https://content.openalex.org/works/W2036271623.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1984810622","https://openalex.org/W2081659888"],"related_works":["https://openalex.org/W3123480064","https://openalex.org/W2561312639","https://openalex.org/W2929286651","https://openalex.org/W4300578962","https://openalex.org/W4297201749","https://openalex.org/W2807523545","https://openalex.org/W3123757586","https://openalex.org/W3008642222","https://openalex.org/W2024590289","https://openalex.org/W2899935356"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
