{"id":"https://openalex.org/W1605749024","doi":"https://doi.org/10.37236/1951","title":"Bounds for the Average $L^p$-Extreme and the $L^\\infty$-Extreme Discrepancy","display_name":"Bounds for the Average $L^p$-Extreme and the $L^\\infty$-Extreme Discrepancy","publication_year":2005,"publication_date":"2005-10-25","ids":{"openalex":"https://openalex.org/W1605749024","doi":"https://doi.org/10.37236/1951","mag":"1605749024"},"language":"en","primary_location":{"id":"doi:10.37236/1951","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1951","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r54/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/v12i1r54/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027293444","display_name":"Michael Gnewuch","orcid":null},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Kiel University","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michael Gnewuch","raw_affiliation_strings":["Mathematisches Seminar, Christian-Albrechts-Universitt Kiel Christian-Albrechts-Platz 4, D-24098 Kiel, Germany","Mathematisches Seminar, Christian-Albrechts-Universit\u00e4t Kiel Christian-Albrechts-Platz 4, D-24098 Kiel, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Seminar, Christian-Albrechts-Universitt Kiel Christian-Albrechts-Platz 4, D-24098 Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]},{"raw_affiliation_string":"Mathematisches Seminar, Christian-Albrechts-Universit\u00e4t Kiel Christian-Albrechts-Platz 4, D-24098 Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5027293444"],"corresponding_institution_ids":["https://openalex.org/I32021983"],"apc_list":null,"apc_paid":null,"fwci":1.7236,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.82889734,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"12","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9997000098228455,"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/unit-cube","display_name":"Unit cube","score":0.8888673782348633},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8570902347564697},{"id":"https://openalex.org/keywords/extreme-point","display_name":"Extreme point","score":0.8220453262329102},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7646306753158569},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6437390446662903},{"id":"https://openalex.org/keywords/extreme-value-theory","display_name":"Extreme value theory","score":0.6406856775283813},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6395122408866882},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.4977896213531494},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4720134437084198},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.46981456875801086},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45311203598976135},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4146053194999695},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19411557912826538},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16529157757759094},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14221793413162231}],"concepts":[{"id":"https://openalex.org/C60432849","wikidata":"https://www.wikidata.org/wiki/Q2072112","display_name":"Unit cube","level":2,"score":0.8888673782348633},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8570902347564697},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.8220453262329102},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7646306753158569},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6437390446662903},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.6406856775283813},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6395122408866882},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.4977896213531494},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4720134437084198},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.46981456875801086},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45311203598976135},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4146053194999695},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19411557912826538},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16529157757759094},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14221793413162231},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1951","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1951","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r54/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:10.37236/1951","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1951","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1r54/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":[{"score":0.4000000059604645,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1605749024.pdf","grobid_xml":"https://content.openalex.org/works/W1605749024.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W152683667","https://openalex.org/W188867022","https://openalex.org/W645185567","https://openalex.org/W1620981000","https://openalex.org/W2036753824","https://openalex.org/W2077597269","https://openalex.org/W2083171368","https://openalex.org/W2138926885","https://openalex.org/W2145441322","https://openalex.org/W4212933304","https://openalex.org/W4249137521","https://openalex.org/W4301425558","https://openalex.org/W6607613993","https://openalex.org/W6621080077"],"related_works":["https://openalex.org/W2031281829","https://openalex.org/W4254427182","https://openalex.org/W2113702600","https://openalex.org/W1999568846","https://openalex.org/W4255848923","https://openalex.org/W2040634226","https://openalex.org/W3189643850","https://openalex.org/W2480729894","https://openalex.org/W2122070455","https://openalex.org/W2952361412"],"abstract_inverted_index":{"The":[0],"extreme":[1],"or":[2],"unanchored":[3],"discrepancy":[4,8,56],"is":[5],"the":[6,13,20,36,51,54,61],"geometric":[7],"of":[9,23,53],"point":[10],"sets":[11],"in":[12],"$d$-dimensional":[14],"unit":[15],"cube":[16],"with":[17,57],"respect":[18],"to":[19,46],"set":[21],"system":[22],"axis-parallel":[24],"boxes.":[25],"For":[26],"$2\\leq":[27],"p":[28],"<":[29],"\\infty$":[30],"we":[31,43],"provide":[32],"upper":[33,48],"bounds":[34,42,49],"for":[35,50],"average":[37],"$L^p$-extreme":[38],"discrepancy.":[39],"With":[40],"these":[41],"are":[44],"able":[45],"derive":[47],"inverse":[52],"$L^\\infty$-extreme":[55],"optimal":[58],"dependence":[59],"on":[60],"dimension":[62],"$d$":[63],"and":[64],"explicitly":[65],"given":[66],"constants.":[67]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}