{"id":"https://openalex.org/W2103882936","doi":"https://doi.org/10.37236/3656","title":"Non-Normal Very Ample Polytopes and their Holes","display_name":"Non-Normal Very Ample Polytopes and their Holes","publication_year":2014,"publication_date":"2014-03-10","ids":{"openalex":"https://openalex.org/W2103882936","doi":"https://doi.org/10.37236/3656","mag":"2103882936"},"language":"en","primary_location":{"id":"doi:10.37236/3656","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3656","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i1p53/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i1p53/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103228742","display_name":"Akihiro Higashitani","orcid":"https://orcid.org/0000-0002-3824-425X"},"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":"Akihiro Higashitani","raw_affiliation_strings":["Osaka University"],"affiliations":[{"raw_affiliation_string":"Osaka University","institution_ids":["https://openalex.org/I98285908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103228742"],"corresponding_institution_ids":["https://openalex.org/I98285908"],"apc_list":null,"apc_paid":null,"fwci":0.5835,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66126802,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"21","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9987000226974487,"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":0.9987000226974487,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9855999946594238,"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/polytope","display_name":"Polytope","score":0.9128226637840271},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7561852931976318},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6776525378227234},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6540558338165283},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6515135765075684},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.4993922710418701},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3247849941253662},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32100316882133484},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16795212030410767},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.15731820464134216},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.09786030650138855}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9128226637840271},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7561852931976318},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6776525378227234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6540558338165283},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6515135765075684},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.4993922710418701},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3247849941253662},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32100316882133484},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16795212030410767},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.15731820464134216},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.09786030650138855}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/3656","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3656","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i1p53/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1208.3955","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1208.3955","pdf_url":"https://arxiv.org/pdf/1208.3955","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":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.755.1767","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.755.1767","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/1208.3955.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1208.3955","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1208.3955","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:2103882936","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.37236/3656","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3656","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i1p53/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3326141890","display_name":null,"funder_award_id":"Research Fellowship for Young Scientist","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3893526170","display_name":null,"funder_award_id":"JSPS Research Fellowship for Young Scientist","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5640883929","display_name":null,"funder_award_id":"Research Fellow","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5701306580","display_name":null,"funder_award_id":"Fellowship for Young Scientists","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7452267826","display_name":null,"funder_award_id":"Research Fellowship for Young Scientists","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8004478673","display_name":null,"funder_award_id":"JSPS Research Fellowship","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8470055433","display_name":null,"funder_award_id":"Research Fellowship","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8485472354","display_name":null,"funder_award_id":"JSPS Research Fellow","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/W2103882936.pdf","grobid_xml":"https://content.openalex.org/works/W2103882936.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W598749360","https://openalex.org/W1701978635","https://openalex.org/W1963547452","https://openalex.org/W2094227518","https://openalex.org/W2108851841","https://openalex.org/W3102864083","https://openalex.org/W3190127111","https://openalex.org/W6698286474","https://openalex.org/W6805483771","https://openalex.org/W6996888795"],"related_works":["https://openalex.org/W2963397268","https://openalex.org/W2085116874","https://openalex.org/W2963705079","https://openalex.org/W2148642357","https://openalex.org/W3118107654","https://openalex.org/W2964030300","https://openalex.org/W167696062","https://openalex.org/W2788867914","https://openalex.org/W2952419021","https://openalex.org/W2014054476","https://openalex.org/W2010859904","https://openalex.org/W3024769167","https://openalex.org/W2092413117","https://openalex.org/W2950031786","https://openalex.org/W2332275131","https://openalex.org/W2477453038","https://openalex.org/W2464153233","https://openalex.org/W3090061977","https://openalex.org/W1848736410","https://openalex.org/W3204693605"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"show":[4],"that":[5],"for":[6],"given":[7],"integers":[8],"$h$":[9,35],"and":[10,16],"$d$":[11,31],"with":[12],"$h":[13],"\\geq":[14,18],"1$":[15],"$d":[17],"3$,":[19],"there":[20],"exists":[21],"a":[22],"non-normal":[23],"very":[24],"ample":[25],"integral":[26],"convex":[27],"polytope":[28],"of":[29],"dimension":[30],"which":[32],"has":[33],"exactly":[34],"holes.":[36]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}