{"id":"https://openalex.org/W7220379792","doi":"https://doi.org/10.48550/arxiv.2610.02450","title":"Hilbert fragments","display_name":"Hilbert fragments","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7220379792","doi":"https://doi.org/10.48550/arxiv.2610.02450"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02450","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02450","pdf_url":"https://arxiv.org/pdf/2610.02450","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.02450","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157382391","display_name":"Csaba Bir\u00f3","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bir\u00f3, Csaba","raw_affiliation_strings":["Department of Mathematics , University of Louisville , Louisville , KY 40220"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Louisville , Louisville , KY 40220","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039000136","display_name":"Andr\u00e9 E. K\u00e9zdy","orcid":"https://orcid.org/0000-0002-5389-6758","observed_orcids":["https://orcid.org/0000-0002-5389-6758"]},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"HUN-REN Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["HU","US"],"is_corresponding":false,"raw_author_name":"K\u00e9zdy, Andr\u00e9 E.","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics , P.O. Box 127 , H-1364 Budapest , Hungary","Department of Mathematics , University of Louisville , Louisville , KY 40220"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics , P.O. Box 127 , H-1364 Budapest , Hungary","institution_ids":["https://openalex.org/I127817813"]},{"raw_affiliation_string":"Department of Mathematics , University of Louisville , Louisville , KY 40220","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157647603","display_name":"Jen\\Ho Lehel","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lehel, Jen\\Ho","raw_affiliation_strings":["Department of Mathematics , University of Louisville , Louisville , KY 40220"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Louisville , Louisville , KY 40220","institution_ids":["https://openalex.org/I142740786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9550999999046326,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9550999999046326,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.027400000020861626,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.014299999922513962,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hilbert-basis","display_name":"Hilbert basis","score":0.7509999871253967},{"id":"https://openalex.org/keywords/interval-orders","display_name":"interval orders","score":0.8629999756813049},{"id":"https://openalex.org/keywords/cocomparability-graphs","display_name":"cocomparability graphs","score":0.9639999866485596},{"id":"https://openalex.org/keywords/intersection-graphs","display_name":"intersection graphs","score":0.9110000133514404},{"id":"https://openalex.org/keywords/binary-vectors","display_name":"binary vectors","score":0.6050000190734863},{"id":"https://openalex.org/keywords/hereditary-graph-properties","display_name":"hereditary graph classes","score":0.7639999985694885},{"id":"https://openalex.org/keywords/one-dimensional-structures","display_name":"one-dimensional structures","score":0.6100000143051147}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6955999732017517},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6819000244140625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5242000222206116},{"id":"https://openalex.org/C76103427","wikidata":"https://www.wikidata.org/wiki/Q5761197","display_name":"Hilbert R-tree","level":5,"score":0.4991999864578247},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.48570001125335693},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.42340001463890076},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4226999878883362},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.4196000099182129},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3919000029563904},{"id":"https://openalex.org/C147493315","wikidata":"https://www.wikidata.org/wiki/Q3554824","display_name":"Hilbert manifold","level":3,"score":0.39079999923706055},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.3869999945163727},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.3781999945640564},{"id":"https://openalex.org/C185982889","wikidata":"https://www.wikidata.org/wiki/Q5761255","display_name":"Hilbert\u2013Poincar\u00e9 series","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.3407000005245209},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C60064506","wikidata":"https://www.wikidata.org/wiki/Q1262627","display_name":"Rigged Hilbert space","level":4,"score":0.29840001463890076},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2874999940395355},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C191326398","wikidata":"https://www.wikidata.org/wiki/Q4515163","display_name":"Hilbert's fourteenth problem","level":5,"score":0.2551000118255615}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02450","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02450","pdf_url":"https://arxiv.org/pdf/2610.02450","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.02450","doi":"https://doi.org/10.48550/arxiv.2610.02450","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02450","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.02450","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02450","pdf_url":"https://arxiv.org/pdf/2610.02450","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220379792.pdf","grobid_xml":"https://content.openalex.org/works/W7220379792.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7133555054","https://openalex.org/W2026407825","https://openalex.org/W207195076","https://openalex.org/W2136941318","https://openalex.org/W2001418923","https://openalex.org/W1965052141","https://openalex.org/W1991248801","https://openalex.org/W1502160615","https://openalex.org/W2019502642","https://openalex.org/W2017814971"],"abstract_inverted_index":{"In":[0],"earlier":[1],"work,":[2],"we":[3],"proved":[4],"that":[5,19],"the":[6,50,87,91,127],"length":[7,98],"polyhedron":[8],"of":[9,22,31,52,60,72,83,93,96],"an":[10,105,121],"interval":[11,133],"order":[12],"has":[13],"a":[14,26,36,43,80,110],"unique":[15],"Hilbert":[16,66,77,102,128],"basis":[17,24],"and":[18,112],"every":[20],"element":[21],"this":[23,117],"is":[25,42],"binary":[27,33],"vector.":[28],"The":[29],"supports":[30,92],"these":[32,73],"vectors":[34],"form":[35,79],"set":[37],"system":[38],"whose":[39],"intersection":[40,58,74,88],"graph":[41],"cocomparability":[44,84],"graph.":[45],"This":[46],"leads":[47],"naturally":[48],"to":[49],"question":[51],"which":[53],"graphs":[54,59,85],"can":[55,119],"arise":[56],"as":[57,69],"such":[61],"Hilbert-basis":[62,94],"supports.":[63],"We":[64,100],"introduce":[65],"fragments,":[67],"defined":[68,107],"induced":[70],"subgraphs":[71],"graphs.":[75,134],"Thus":[76],"fragments":[78,103,129],"hereditary":[81],"class":[82],"recording":[86],"patterns":[89],"among":[90],"elements":[95],"interval-order":[97],"polyhedra.":[99],"characterize":[101],"by":[104],"axiomatically":[106],"vertex-labeling,":[108],"called":[109],"track-labeling,":[111],"give":[113],"applications":[114],"illustrating":[115],"how":[116],"characterization":[118],"reveal":[120],"underlying":[122],"one-dimensional":[123],"structure":[124],"even":[125],"when":[126],"themselves":[130],"are":[131],"not":[132]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-06T00:00:00"}
