{"id":"https://openalex.org/W4401646223","doi":"https://doi.org/10.1007/s10623-024-01480-0","title":"On the maximum size of ultrametric orthogonal sets over discrete valued fields","display_name":"On the maximum size of ultrametric orthogonal sets over discrete valued fields","publication_year":2024,"publication_date":"2024-08-16","ids":{"openalex":"https://openalex.org/W4401646223","doi":"https://doi.org/10.1007/s10623-024-01480-0"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-024-01480-0","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10623-024-01480-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-024-01480-0.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-024-01480-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000635652","display_name":"Noy Soffer Aranov","orcid":"https://orcid.org/0009-0005-1978-4073"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Noy Soffer Aranov","raw_affiliation_strings":["Department of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043941712","display_name":"Angelot Behajaina","orcid":"https://orcid.org/0000-0002-7912-4238"},"institutions":[{"id":"https://openalex.org/I164950643","display_name":"Open University of Israel","ror":"https://ror.org/027z64205","country_code":"IL","type":"education","lineage":["https://openalex.org/I164950643"]},{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Angelot Behajaina","raw_affiliation_strings":["Department of Mathematics and Computer Science, The Open University of Israel, Ra\u2019anana, Israel","Department of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, The Open University of Israel, Ra\u2019anana, Israel","institution_ids":["https://openalex.org/I164950643"]},{"raw_affiliation_string":"Department of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000635652"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.8119,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.82937915,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"92","issue":"12","first_page":"4035","last_page":"4055"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.9987999796867371,"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/T13234","display_name":"advanced mathematical theories","score":0.9987999796867371,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9760000109672546,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9699000120162964,"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/ultrametric-space","display_name":"Ultrametric space","score":0.956218421459198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8827434778213501},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4830653965473175},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43453627824783325},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.10110276937484741}],"concepts":[{"id":"https://openalex.org/C61067352","wikidata":"https://www.wikidata.org/wiki/Q1897429","display_name":"Ultrametric space","level":3,"score":0.956218421459198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8827434778213501},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4830653965473175},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43453627824783325},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.10110276937484741}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10623-024-01480-0","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10623-024-01480-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-024-01480-0.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2408.12019","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2408.12019","pdf_url":"https://arxiv.org/pdf/2408.12019","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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-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":"text"}],"best_oa_location":{"id":"doi:10.1007/s10623-024-01480-0","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10623-024-01480-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-024-01480-0.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323721","display_name":"Technion-Israel Institute of Technology","ror":"https://ror.org/03qryx823"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401646223.pdf","grobid_xml":"https://content.openalex.org/works/W4401646223.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1535387186","https://openalex.org/W1999663691","https://openalex.org/W2000304127","https://openalex.org/W2080598978","https://openalex.org/W2132615501","https://openalex.org/W2151817671","https://openalex.org/W2162194912","https://openalex.org/W2319446899","https://openalex.org/W2604980646","https://openalex.org/W2609005943","https://openalex.org/W2963606849","https://openalex.org/W2990152272","https://openalex.org/W3105204421","https://openalex.org/W3126144012"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4395449128","https://openalex.org/W4287598215","https://openalex.org/W3105794585","https://openalex.org/W4236333616","https://openalex.org/W2999666600","https://openalex.org/W2054856023","https://openalex.org/W4245978557","https://openalex.org/W4285726363","https://openalex.org/W1612061217"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"$${\\mathcal":[2,46],"{K}}$$":[3],"<mml:math":[4,27,48,78,103,131,148,160],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[5,28,49,79,104,132,149,161],"<mml:mi>K</mml:mi>":[6,52,110],"</mml:math>":[7,35,56,87,121,138,155,163],"be":[8],"a":[9,39,63,95],"discrete":[10],"valued":[11],"field":[12],"with":[13,19],"finite":[14],"residue":[15],"field.":[16],"In":[17,58],"analogy":[18],"orthogonality":[20],"in":[21,45,67,170],"the":[22,68,91,123],"Euclidean":[23],"space":[24],"$${\\mathbb":[25],"{R}}^n$$":[26],"<mml:msup>":[29,50,108],"<mml:mrow>":[30,51,80,105,109,115,133,150],"<mml:mi>R</mml:mi>":[31],"</mml:mrow>":[32,53,86,111,119,120,137,154],"<mml:mi>n</mml:mi>":[33,54,112],"</mml:msup>":[34,55,113],",":[36,88,142],"there":[37,143],"is":[38],"well-studied":[40],"notion":[41],"of":[42,65,94,139,156,176],"\u201cultrametric":[43],"orthogonality\u201d":[44],"{K}}^n$$":[47],".":[57],"this":[59,177],"paper,":[60],"motivated":[61],"by":[62],"question":[64],"Erd\u0151s":[66],"real":[69],"case,":[70],"given":[71],"integers":[72],"$$k":[73],"\\ge":[74,76],"\\ell":[75],"2$$":[77],"<mml:mi>k</mml:mi>":[81],"<mml:mo>\u2265</mml:mo>":[82,84],"<mml:mi>\u2113</mml:mi>":[83,162],"<mml:mn>2</mml:mn>":[85],"we":[89],"investigate":[90],"maximum":[92],"size":[93,140,157],"subset":[96],"$$S":[97],"\\subseteq":[98,129,146],"{\\mathcal":[99],"{K}}^n":[100],"{\\setminus":[101],"}\\{\\textbf{0}\\}$$":[102],"<mml:mi>S</mml:mi>":[106,136],"<mml:mo>\u2286</mml:mo>":[107,135,152],"<mml:mo>\\</mml:mo>":[114],"<mml:mo>{</mml:mo>":[116],"<mml:mn>0</mml:mn>":[117],"<mml:mo>}</mml:mo>":[118],"satisfying":[122],"following":[124],"property:":[125],"for":[126],"any":[127,166],"$$E":[128],"S$$":[130],"<mml:mi>E</mml:mi>":[134,153],"k":[141],"exists":[144],"$$F":[145],"E$$":[147],"<mml:mi>F</mml:mi>":[151],"$$\\ell":[158],"$$":[159],"such":[164],"that":[165],"two":[167],"distinct":[168],"vectors":[169],"F":[171],"are":[172,179],"orthogonal.":[173],"Other":[174],"variants":[175],"property":[178],"also":[180],"studied.":[181]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2024-08-17T00:00:00"}
