{"id":"https://openalex.org/W2767599137","doi":"https://doi.org/10.37236/105","title":"An Alternative Definition of the Notion Valuation in the Theory of Near Polygons","display_name":"An Alternative Definition of the Notion Valuation in the Theory of Near Polygons","publication_year":2009,"publication_date":"2009-01-30","ids":{"openalex":"https://openalex.org/W2767599137","doi":"https://doi.org/10.37236/105","mag":"2767599137"},"language":"en","primary_location":{"id":"doi:10.37236/105","is_oa":true,"landing_page_url":"https://doi.org/10.37236/105","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r16/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r16/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075866833","display_name":"Bart De Bruyn","orcid":"https://orcid.org/0000-0003-4941-7934"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Bart De Bruyn","raw_affiliation_strings":["Department of Pure Mathematics and Computer Algebra Ghent University, Gent, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Computer Algebra Ghent University, Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075866833"],"corresponding_institution_ids":["https://openalex.org/I32597200"],"apc_list":null,"apc_paid":null,"fwci":2.3503,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87706612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9997000098228455,"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/T10849","display_name":"Finite Group Theory Research","score":0.9997000098228455,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9923999905586243,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8398305177688599},{"id":"https://openalex.org/keywords/valuation","display_name":"Valuation (finance)","score":0.7412958145141602},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6785911321640015},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6609731316566467},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.508588433265686},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.49600252509117126},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.410614550113678},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19908985495567322},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1369396150112152},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10110348463058472}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8398305177688599},{"id":"https://openalex.org/C186027771","wikidata":"https://www.wikidata.org/wiki/Q4008379","display_name":"Valuation (finance)","level":2,"score":0.7412958145141602},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6785911321640015},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6609731316566467},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.508588433265686},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.49600252509117126},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.410614550113678},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19908985495567322},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1369396150112152},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10110348463058472},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/105","is_oa":true,"landing_page_url":"https://doi.org/10.37236/105","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r16/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:archive.ugent.be:879114","is_oa":true,"landing_page_url":"http://hdl.handle.net/1854/LU-879114","pdf_url":"https://biblio.ugent.be/publication/879114/file/879145.pdf","source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1077-8926","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.37236/105","is_oa":true,"landing_page_url":"https://doi.org/10.37236/105","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r16/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2767599137.pdf","grobid_xml":"https://content.openalex.org/works/W2767599137.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W122599093","https://openalex.org/W1538797557","https://openalex.org/W1583183878","https://openalex.org/W1973275955","https://openalex.org/W1999305531","https://openalex.org/W2029093857","https://openalex.org/W2042469674","https://openalex.org/W2063445159","https://openalex.org/W2086350895","https://openalex.org/W2108226886","https://openalex.org/W4241138392","https://openalex.org/W6676114605"],"related_works":["https://openalex.org/W2993985424","https://openalex.org/W1587621605","https://openalex.org/W1598828859","https://openalex.org/W1515228725","https://openalex.org/W1990862705","https://openalex.org/W2133183039","https://openalex.org/W1957367071","https://openalex.org/W3036781944","https://openalex.org/W2074852225","https://openalex.org/W2904264866","https://openalex.org/W2028179220","https://openalex.org/W2026157097","https://openalex.org/W2083159437","https://openalex.org/W2044776122","https://openalex.org/W2066037950","https://openalex.org/W1534142191","https://openalex.org/W421695236","https://openalex.org/W1606204101","https://openalex.org/W1655943735","https://openalex.org/W1649547313"],"abstract_inverted_index":{"Valuations":[0],"of":[1,11,30,38,50,53,65,79],"dense":[2,13,87],"near":[3,14,88],"polygons":[4],"were":[5],"introduced":[6],"in":[7],"[9].":[8],"A":[9],"valuation":[10,68],"a":[12,22],"polygon":[15],"${\\cal":[16,28,31,54],"S}=({\\cal":[17],"P},{\\cal":[18],"L},{\\rm":[19],"I})$":[20],"is":[21],"map":[23],"$f$":[24],"from":[25],"the":[26,34,48,57,66,77],"point-set":[27],"P}$":[29],"S}$":[32],"to":[33,47],"set":[35,49],"$\\Bbb":[36],"N$":[37],"nonnegative":[39],"integers":[40],"satisfying":[41],"very":[42],"nice":[43],"properties":[44],"with":[45],"respect":[46],"convex":[51],"subspaces":[52],"S}$.":[55],"In":[56,76],"present":[58],"paper,":[59],"we":[60],"give":[61],"an":[62],"alternative":[63,91],"definition":[64,92],"notion":[67],"and":[69,83],"prove":[70],"that":[71],"both":[72],"definitions":[73],"are":[74],"equivalent.":[75],"case":[78],"dual":[80],"polar":[81],"spaces":[82],"many":[84],"other":[85],"known":[86],"polygons,":[89],"this":[90],"can":[93],"be":[94],"significantly":[95],"simplified.":[96]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
