{"id":"https://openalex.org/W7114800512","doi":"https://doi.org/10.37236/12756","title":"Covering the Hypercube, the Uncertainty Principle, and an Interpolation Formula","display_name":"Covering the Hypercube, the Uncertainty Principle, and an Interpolation Formula","publication_year":2025,"publication_date":"2025-12-11","ids":{"openalex":"https://openalex.org/W7114800512","doi":"https://doi.org/10.37236/12756"},"language":null,"primary_location":{"id":"doi:10.37236/12756","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12756","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i4p69/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v32i4p69/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Paata Ivanisvili","orcid":null},"institutions":[{"id":"https://openalex.org/I149910238","display_name":"Kent State University","ror":"https://ror.org/049pfb863","country_code":"US","type":"education","lineage":["https://openalex.org/I149910238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paata Ivanisvili","raw_affiliation_strings":["Kent State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kent State University","institution_ids":["https://openalex.org/I149910238"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ohad Klein","orcid":null},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ohad Klein","raw_affiliation_strings":["Hebrew University of Jerusalem"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hebrew University of Jerusalem","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":null,"display_name":"Roman Vershynin","orcid":null},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Roman Vershynin","raw_affiliation_strings":["University of California, Irvine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Irvine","institution_ids":["https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.63729742,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.37220001220703125,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.37220001220703125,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.14419999718666077,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.06069999933242798,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.7760999798774719},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.707099974155426},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6360999941825867},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5999000072479248},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.5853000283241272},{"id":"https://openalex.org/keywords/multilinear-map","display_name":"Multilinear map","score":0.5677000284194946},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.48559999465942383},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.47440001368522644}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8575000166893005},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.7760999798774719},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.707099974155426},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6360999941825867},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5999000072479248},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.5853000283241272},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.5677000284194946},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.48559999465942383},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48510000109672546},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47440001368522644},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47380000352859497},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.42340001463890076},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.3767000138759613},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3582000136375427},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.3537999987602234},{"id":"https://openalex.org/C46132437","wikidata":"https://www.wikidata.org/wiki/Q6901742","display_name":"Monomial basis","level":3,"score":0.31470000743865967},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C28537468","wikidata":"https://www.wikidata.org/wiki/Q464356","display_name":"Trigonometric interpolation","level":5,"score":0.28450000286102295},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.27549999952316284},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.266400009393692}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/12756","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12756","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i4p69/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:10.37236/12756","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12756","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i4p69/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3112551100","display_name":null,"funder_award_id":"DMS-2027299","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7361187543","display_name":null,"funder_award_id":"1774/20","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G7796262111","display_name":"CAREER: Discrete Structures and Orthogonal Systems","funder_award_id":"2152401","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G835903323","display_name":null,"funder_award_id":"DMS-1954233","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8746953091","display_name":"Collaborative Research:  A Mathematical Framework for Generating Synthetic Data","funder_award_id":"2027299","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8945958279","display_name":"High-Dimensional Probability for High-Dimensional Data","funder_award_id":"1954233","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7114800512.pdf","grobid_xml":"https://content.openalex.org/works/W7114800512.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,9,69],"the":[3,11,25,42,46,74,87,90],"minimal":[4,35],"number":[5],"of":[6,60,84,86],"skewed":[7,32],"hyperplanes":[8],"cover":[10],"hypercube":[12,26],"$\\{0,1\\}^{n}$":[13,92],"is":[14],"at":[15],"least":[16],"$\\frac{n}{2}+1$,":[17],"and":[18],"there":[19],"are":[20,38,96],"infinitely":[21],"many":[22],"$n$'s":[23],"when":[24],"can":[27,77],"be":[28,78],"covered":[29],"with":[30],"$n-\\log_{2}(n)+1$":[31],"hyperplanes.":[33],"The":[34],"covering":[36],"problems":[37],"closely":[39],"related":[40],"to":[41,73],"uncertainty":[43],"principle":[44],"on":[45,58],"hypercube,":[47],"where":[48],"we":[49],"also":[50],"obtain":[51],"an":[52],"interpolation":[53],"formula":[54],"for":[55],"multilinear":[56],"polynomials":[57],"$\\mathbb{R}^{n}$":[59],"degree":[61],"less":[62],"than":[63],"$\\lfloor":[64],"n/m":[65],"\\rfloor$":[66],"by":[67,98],"showing":[68],"its":[70],"coefficients":[71],"corresponding":[72],"largest":[75],"monomials":[76],"represented":[79],"as":[80],"a":[81],"linear":[82],"combination":[83],"values":[85],"polynomial":[88],"over":[89],"points":[91],"whose":[93],"Hamming":[94],"weights":[95],"divisible":[97],"$m$.":[99]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-12-11T00:00:00"}
