{"id":"https://openalex.org/W3088612125","doi":"https://doi.org/10.1007/s00454-023-00506-z","title":"A Uniform Lower Bound on the Norms of Hyperplane Projections of Spherical Polytopes","display_name":"A Uniform Lower Bound on the Norms of Hyperplane Projections of Spherical Polytopes","publication_year":2023,"publication_date":"2023-04-19","ids":{"openalex":"https://openalex.org/W3088612125","doi":"https://doi.org/10.1007/s00454-023-00506-z","mag":"3088612125"},"language":"lv","primary_location":{"id":"doi:10.1007/s00454-023-00506-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00506-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00506-z.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00506-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066589324","display_name":"Tomasz Kobos","orcid":"https://orcid.org/0000-0002-1571-5549"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Tomasz Kobos","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Jagiellonian University, \u0141ojasiewicza 6, 30-348, Krak\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0002-1571-5549","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Jagiellonian University, \u0141ojasiewicza 6, 30-348, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066589324"],"corresponding_institution_ids":["https://openalex.org/I126596746"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00375907,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"1","first_page":"279","last_page":"296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9957000017166138,"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"}},"topics":[{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.982200026512146,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5341203808784485},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.4434872269630432},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25009095668792725},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24362626671791077},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23318326473236084}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5341203808784485},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.4434872269630432},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25009095668792725},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24362626671791077},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23318326473236084}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-023-00506-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00506-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00506-z.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:ruj.uj.edu.pl:item/326029","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/xmlui/handle/item/326029","pdf_url":"http://ruj.uj.edu.pl/bitstreams/76894e80-5a8e-4280-9764-e5e859a49e13/download","source":{"id":"https://openalex.org/S4306400316","display_name":"Homo Politicus (Academy of Humanities and Economics in Lodz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"artyku\u0142 w czasopi\u015bmie"}],"best_oa_location":{"id":"doi:10.1007/s00454-023-00506-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00506-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00506-z.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3088612125.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1039628073","https://openalex.org/W1539416424","https://openalex.org/W1557519337","https://openalex.org/W1742030921","https://openalex.org/W1975049815","https://openalex.org/W1975341768","https://openalex.org/W1990610709","https://openalex.org/W2004099860","https://openalex.org/W2005407846","https://openalex.org/W2020818868","https://openalex.org/W2021409937","https://openalex.org/W2073317766","https://openalex.org/W2093369319","https://openalex.org/W2094442586","https://openalex.org/W2288682671","https://openalex.org/W2316383984","https://openalex.org/W2327480601","https://openalex.org/W2332422908","https://openalex.org/W2478845337","https://openalex.org/W2527816160","https://openalex.org/W2913102136","https://openalex.org/W2950188745","https://openalex.org/W2963349025","https://openalex.org/W2963800846","https://openalex.org/W3047298799","https://openalex.org/W4248101252"],"related_works":["https://openalex.org/W3024295069","https://openalex.org/W2115296315","https://openalex.org/W4206584845","https://openalex.org/W3139225106","https://openalex.org/W2103535553","https://openalex.org/W2005713764","https://openalex.org/W1762008180","https://openalex.org/W4312865284","https://openalex.org/W2030506963","https://openalex.org/W1553352381"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"K":[2,87,104],"be":[3],"a":[4,14,51],"centrally":[5],"symmetric":[6],"spherical":[7],"and":[8,101,125],"simplicial":[9],"polytope,":[10],"whose":[11],"vertices":[12,100],"form":[13],"$$(4n)^{-1}$$":[15],"<mml:math":[16,39,64,111,131,170,208,225,268,282],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[17,40,65,112,132,171,209,226,269,283],"<mml:msup>":[18,41,116,243,249],"<mml:mrow>":[19,25,42,66,113,118,133,136,141,172,210,227,229,245,284],"<mml:mo>(</mml:mo>":[20,247],"<mml:mn>4</mml:mn>":[21,119,254],"<mml:mi>n</mml:mi>":[22,45,117,120,241,250,255,272],"<mml:mo>)</mml:mo>":[23,258],"</mml:mrow>":[24,28,44,72,121,123,140,163,164,189,216,233,259,261,290],"<mml:mo>-</mml:mo>":[26,246,286],"<mml:mn>1</mml:mn>":[27,146,175,237,285],"</mml:msup>":[29,46,122,252,260],"</mml:math>":[30,47,73,124,165,190,217,262,274,291],"-net":[31],"in":[32,36,93,197],"the":[33,56,78,84,96,198,277],"unit":[34,85,199],"sphere":[35],"$${\\mathbb":[37],"R}^n$$":[38],"<mml:mi>R</mml:mi>":[43],".":[48,88,105,292],"We":[49],"prove":[50],"uniform":[52],"lower":[53],"bound":[54],"on":[55],"norms":[57],"of":[58,95,99,103],"all":[59],"hyperplane":[60,203],"projections":[61],"$$P:X\\rightarrow":[62],"X$$":[63,207],"<mml:mi>P</mml:mi>":[67,211,231],"<mml:mo>:</mml:mo>":[68,212],"<mml:mi>X</mml:mi>":[69,71,213,215,234],"<mml:mo>\u2192</mml:mo>":[70,214],",":[74,166],"where":[75,167],"X":[76],"is":[77,91],"n":[79],"-dimensional":[80],"normed":[81],"space":[82],"with":[83,276],"ball":[86],"The":[89],"estimate":[90],"given":[92],"terms":[94],"determinant":[97],"function":[98],"faces":[102],"In":[106],"particular,":[107],"if":[108],"$$N\\ge":[109],"n^{4n}$$":[110],"<mml:mi>N</mml:mi>":[114,160,187,244,289],"<mml:mo>\u2265</mml:mo>":[115,236],"$$K={{\\,\\textrm{conv}\\,}}{\\{\\pm":[126],"x_1,\\pm":[127],"x_2,\\dots":[128],",\\pm":[129],"x_N\\}}$$":[130],"<mml:mi>K</mml:mi>":[134],"<mml:mo>=</mml:mo>":[135],"<mml:mspace/>":[137,139],"<mml:mtext>conv</mml:mtext>":[138],"<mml:mo>{</mml:mo>":[142],"<mml:mo>\u00b1</mml:mo>":[143,149,157],"<mml:msub>":[144,150,158,173,178,185,228,239,270],"<mml:mi>x</mml:mi>":[145,151,159,174,179,186],"</mml:msub>":[147,153,161,176,181,188,235,242,273],"<mml:mo>,</mml:mo>":[148,154,156,177,182,184],"<mml:mn>2</mml:mn>":[152,180,248,251],"<mml:mo>\u22ef</mml:mo>":[155,183],"<mml:mo>}</mml:mo>":[162],"$$x_1,x_2,\\dots":[168],",x_N$$":[169],"are":[191],"independent":[192],"random":[193],"points":[194],"distributed":[195],"uniformly":[196],"sphere,":[200],"then":[201],"every":[202],"projection":[204],"$$P:X":[205],"\\rightarrow":[206],"satisfies":[218],"an":[219],"inequality":[220],"$$\\Vert":[221],"P\\Vert":[222],"_X\\ge":[223],"1+c_nN^{-(2n^2+4n+6)}$$":[224],"<mml:mo>\u2016</mml:mo>":[230,232],"<mml:mo>+</mml:mo>":[238,253,256],"<mml:mi>c</mml:mi>":[240,271],"<mml:mn>6</mml:mn>":[257],"(for":[263],"some":[264],"explicit":[265],"constant":[266],"$$c_n$$":[267],"),":[275],"probability":[278],"at":[279],"least":[280],"$$1-3/N$$":[281],"<mml:mn>3</mml:mn>":[287],"<mml:mo>/</mml:mo>":[288]},"counts_by_year":[],"updated_date":"2026-08-02T14:50:37.381335","created_date":"2025-10-10T00:00:00"}