{"id":"https://openalex.org/W7208790276","doi":"https://doi.org/10.48550/arxiv.2609.03200","title":"Stability of maximal relative projection constants","display_name":"Stability of maximal relative projection constants","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7208790276","doi":"https://doi.org/10.48550/arxiv.2609.03200"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.03200","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03200","pdf_url":"https://arxiv.org/pdf/2609.03200","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/2609.03200","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120981531","display_name":"Hitesh Kumar","orcid":"https://orcid.org/0009-0007-5016-0159","observed_orcids":["https://orcid.org/0009-0007-5016-0159"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kumar, Hitesh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005993212","display_name":"Bojan Mohar","orcid":"https://orcid.org/0000-0002-7408-6148","observed_orcids":["https://orcid.org/0000-0002-7408-6148"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mohar, Bojan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034297355","display_name":"Seyed Ahmad Mojallal","orcid":"https://orcid.org/0000-0002-8129-2644","observed_orcids":["https://orcid.org/0000-0002-8129-2644"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mojallal, Seyed Ahmad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5052555886","display_name":"Shivaramakrishna Pragada","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pragada, Shivaramakrishna","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0026000000070780516,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.0008999999845400453,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/l-infinity-spaces","display_name":"L-infinity spaces","score":0.718999981880188},{"id":"https://openalex.org/keywords/finite-dimensional-subspaces","display_name":"finite-dimensional subspaces","score":0.8330000042915344},{"id":"https://openalex.org/keywords/banach-spaces","display_name":"Banach spaces","score":0.46700000762939453}],"concepts":[{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.7851999998092651},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7807000279426575},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.718500018119812},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5978000164031982},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5351999998092651},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5299999713897705},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46860000491142273},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3928000032901764},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.38830000162124634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31690001487731934},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.27469998598098755},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.25200000405311584},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.03200","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03200","pdf_url":"https://arxiv.org/pdf/2609.03200","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.03200","doi":"https://doi.org/10.48550/arxiv.2609.03200","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.03200","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.03200","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03200","pdf_url":"https://arxiv.org/pdf/2609.03200","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1866363149","display_name":null,"funder_award_id":"R832714","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G5099342464","display_name":null,"funder_award_id":"101071836","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8787022471","display_name":null,"funder_award_id":"N1-0218","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7208790276.pdf","grobid_xml":"https://content.openalex.org/works/W7208790276.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4414857724","https://openalex.org/W7148251236","https://openalex.org/W7172451143","https://openalex.org/W7172509980"],"related_works":["https://openalex.org/W1997456455","https://openalex.org/W2092693975","https://openalex.org/W4322576768","https://openalex.org/W1995844989","https://openalex.org/W2527816160","https://openalex.org/W1819815372","https://openalex.org/W2163406986","https://openalex.org/W2061375263","https://openalex.org/W2145807473","https://openalex.org/W3172493407"],"abstract_inverted_index":{"For":[0],"positive":[1],"integers":[2],"$n\\ge":[3],"r$,":[4],"let":[5],"$\u03bb(r,n)$":[6,35,51],"denote":[7,20],"the":[8,21],"\\emph{maximal":[9,22],"relative":[10],"projection":[11,24],"constant}":[12],"of":[13,16,75,81],"$r$-dimensional":[14],"subspaces":[15],"$\\ell_\\infty^n$":[17],"and":[18],"$\u03bb(r)$":[19,42,54],"absolute":[23],"constant},":[25],"respectively.":[26],"It":[27],"is":[28,36,49,80],"known":[29],"that":[30,60],"for":[31,55,61],"any":[32,62],"fixed":[33,63],"$r$,":[34,64],"a":[37,73],"non-decreasing":[38],"sequence":[39],"with":[40],"limit":[41],"as":[43],"$n\\to":[44],"\\infty$.":[45],"A":[46],"natural":[47],"question":[48,74],"whether":[50],"stabilizes":[52],"at":[53],"some":[56],"$n>r$.":[57],"We":[58],"prove":[59],"\\[\u03bb(r,n)=\u03bb(r)":[65],"\\qquad":[66],"\\text{for":[67],"every}\\qquad":[68],"n\\ge":[69],"2^{r}\\binom{r+1}{2}.\\]":[70],"This":[71],"answers":[72],"Basso.":[76],"The":[77],"technique":[78],"used":[79],"independent":[82],"interest.":[83]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-05T00:00:00"}