{"id":"https://openalex.org/W1975436244","doi":"https://doi.org/10.1007/s10107-009-0280-y","title":"Representing simple d-dimensional polytopes by d polynomials","display_name":"Representing simple d-dimensional polytopes by d polynomials","publication_year":2009,"publication_date":"2009-04-15","ids":{"openalex":"https://openalex.org/W1975436244","doi":"https://doi.org/10.1007/s10107-009-0280-y","mag":"1975436244"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-009-0280-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-009-0280-y","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5020875207","display_name":"Gennadiy Averkov","orcid":"https://orcid.org/0000-0003-2245-9958"},"institutions":[{"id":"https://openalex.org/I4210138551","display_name":"University Hospital Magdeburg","ror":"https://ror.org/03m04df46","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I4210138551"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Gennadiy Averkov","raw_affiliation_strings":["Faculty of Mathematics, University of Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","University of Magdeburg, Faculty of Mathematics, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","institution_ids":["https://openalex.org/I4210138551"]},{"raw_affiliation_string":"University of Magdeburg, Faculty of Mathematics, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany#TAB#","institution_ids":["https://openalex.org/I4210138551"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040119486","display_name":"Martin Henk","orcid":"https://orcid.org/0000-0003-1411-3033"},"institutions":[{"id":"https://openalex.org/I4210138551","display_name":"University Hospital Magdeburg","ror":"https://ror.org/03m04df46","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I4210138551"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Henk","raw_affiliation_strings":["Faculty of Mathematics, University of Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","University of Magdeburg, Faculty of Mathematics, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","institution_ids":["https://openalex.org/I4210138551"]},{"raw_affiliation_string":"University of Magdeburg, Faculty of Mathematics, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany#TAB#","institution_ids":["https://openalex.org/I4210138551"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020875207"],"corresponding_institution_ids":["https://openalex.org/I4210138551"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.39,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.8559206,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"126","issue":"2","first_page":"203","last_page":"230"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9976000189781189,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9941999912261963,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.9336256980895996},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.816496729850769},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8127977848052979},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6644611954689026},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6191688776016235},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6144299507141113},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.5801555514335632},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5160602927207947},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3396141231060028},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.3001869320869446},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13809961080551147},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.12995418906211853},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09403499960899353}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9336256980895996},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.816496729850769},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8127977848052979},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6644611954689026},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6191688776016235},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6144299507141113},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.5801555514335632},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5160602927207947},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3396141231060028},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.3001869320869446},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13809961080551147},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.12995418906211853},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09403499960899353},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10107-009-0280-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-009-0280-y","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.245.734","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.245.734","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/0709.2099v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.84.6361","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.84.6361","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://fma2.math.uni-magdeburg.de/~averkov/publications/AverkovHenkRepresentingSimplePolytopesbyPolynomialsSubmission.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W74058400","https://openalex.org/W1491777560","https://openalex.org/W1500527210","https://openalex.org/W1571966798","https://openalex.org/W1574151794","https://openalex.org/W1597196612","https://openalex.org/W1963601817","https://openalex.org/W1970367947","https://openalex.org/W1978625388","https://openalex.org/W2013348732","https://openalex.org/W2020586320","https://openalex.org/W2035135883","https://openalex.org/W2035142318","https://openalex.org/W2037009101","https://openalex.org/W2047577886","https://openalex.org/W2066181227","https://openalex.org/W2166156256","https://openalex.org/W2398566424","https://openalex.org/W2951555161","https://openalex.org/W2971235269","https://openalex.org/W4241645483","https://openalex.org/W4247890365","https://openalex.org/W4255213956","https://openalex.org/W4300166240","https://openalex.org/W6602301541","https://openalex.org/W6611256690"],"related_works":["https://openalex.org/W4287022798","https://openalex.org/W2884061808","https://openalex.org/W4226058339","https://openalex.org/W2901329027","https://openalex.org/W4221156915","https://openalex.org/W1990911204","https://openalex.org/W2069107464","https://openalex.org/W2768257653","https://openalex.org/W2557288725","https://openalex.org/W3012067785"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
