{"id":"https://openalex.org/W1559089952","doi":"https://doi.org/10.37236/1102","title":"The Valuations of the Near Octagon ${\\Bbb I}_4$","display_name":"The Valuations of the Near Octagon ${\\Bbb I}_4$","publication_year":2006,"publication_date":"2006-08-25","ids":{"openalex":"https://openalex.org/W1559089952","doi":"https://doi.org/10.37236/1102","mag":"1559089952"},"language":"en","primary_location":{"id":"doi:10.37236/1102","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1102","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r76/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/v13i1r76/pdf","any_repository_has_fulltext":false},"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/I2802067006","display_name":"Research Foundation - Flanders","ror":"https://ror.org/03qtxy027","country_code":"BE","type":"government","lineage":["https://openalex.org/I2802067006"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Bart De Bruyn","raw_affiliation_strings":["Postdoctoral Fellow of the Research Foundation -Flanders"],"affiliations":[{"raw_affiliation_string":"Postdoctoral Fellow of the Research Foundation -Flanders","institution_ids":["https://openalex.org/I2802067006"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089419115","display_name":"Pieter Vandecasteele","orcid":null},"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":false,"raw_author_name":"Pieter Vandecasteele","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":2,"corresponding_author_ids":["https://openalex.org/A5075866833"],"corresponding_institution_ids":["https://openalex.org/I2802067006"],"apc_list":null,"apc_paid":null,"fwci":0.4689,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55728242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","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":0.9991000294685364,"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":0.9991000294685364,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9860000014305115,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.8711841106414795},{"id":"https://openalex.org/keywords/quadric","display_name":"Quadric","score":0.7737009525299072},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.6872391700744629},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6644046306610107},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6093505024909973},{"id":"https://openalex.org/keywords/valuation","display_name":"Valuation (finance)","score":0.5882498621940613},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.5732874274253845},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5549091100692749},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3682730197906494},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28053075075149536},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.06979221105575562},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06036776304244995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8711841106414795},{"id":"https://openalex.org/C2779219049","wikidata":"https://www.wikidata.org/wiki/Q852117","display_name":"Quadric","level":2,"score":0.7737009525299072},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.6872391700744629},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6644046306610107},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6093505024909973},{"id":"https://openalex.org/C186027771","wikidata":"https://www.wikidata.org/wiki/Q4008379","display_name":"Valuation (finance)","level":2,"score":0.5882498621940613},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5732874274253845},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5549091100692749},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3682730197906494},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28053075075149536},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.06979221105575562},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06036776304244995},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1102","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1102","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r76/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"}],"best_oa_location":{"id":"doi:10.37236/1102","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1102","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r76/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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1559089952.pdf","grobid_xml":"https://content.openalex.org/works/W1559089952.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1583183878","https://openalex.org/W1973275955","https://openalex.org/W1974319441","https://openalex.org/W1999587863","https://openalex.org/W2008905407","https://openalex.org/W2009807169","https://openalex.org/W2042469674","https://openalex.org/W2059502634","https://openalex.org/W2063445159","https://openalex.org/W2071896100","https://openalex.org/W2108226886","https://openalex.org/W2395930029","https://openalex.org/W4213292753","https://openalex.org/W6676114605"],"related_works":["https://openalex.org/W2384882317","https://openalex.org/W2037264771","https://openalex.org/W2950567443","https://openalex.org/W2327777938","https://openalex.org/W2116952306","https://openalex.org/W3017621005","https://openalex.org/W1660957572","https://openalex.org/W1982642009","https://openalex.org/W2610981215","https://openalex.org/W1496466047"],"abstract_inverted_index":{"The":[0],"maximal":[1],"and":[2,66,106],"next-to-maximal":[3],"subspaces":[4],"of":[5,33,45,50,60,76,95,100],"a":[6,19,27,48,74,90],"nonsingular":[7],"parabolic":[8],"quadric":[9,22],"$Q(2n,2)$,":[10],"$n":[11],"\\geq":[12],"2$,":[13],"which":[14],"are":[15,70],"not":[16],"contained":[17],"in":[18],"given":[20],"hyperbolic":[21],"$Q^+(2n-1,2)":[23],"\\subset":[24],"Q(2n,2)$":[25],"define":[26],"sub":[28],"near":[29,62],"polygon":[30],"${\\Bbb":[31,51,64,96],"I}_n$":[32,97],"the":[34,61,101],"dual":[35,102],"polar":[36,103],"space":[37],"$DQ(2n,2)$.":[38],"It":[39],"is":[40],"known":[41],"that":[42,68,84],"every":[43],"valuation":[44,49,75],"$DQ(2n,2)$":[46,105],"induces":[47],"I}_n$.":[52],"In":[53],"this":[54,80],"paper,":[55],"we":[56],"classify":[57],"all":[58,71],"valuations":[59],"octagon":[63],"I}_4$":[65],"show":[67,83],"they":[69],"induced":[72],"by":[73],"$DQ(8,2)$.":[77],"We":[78],"use":[79],"classification":[81],"to":[82,88],"there":[85],"exists":[86],"up":[87],"isomorphism":[89],"unique":[91],"isometric":[92],"full":[93],"embedding":[94],"into":[98],"each":[99],"spaces":[104],"$DH(2n-1,4)$.":[107]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
