{"id":"https://openalex.org/W4389207817","doi":"https://doi.org/10.37236/11651","title":"On Hierarchically Closed Fractional Intersecting Families","display_name":"On Hierarchically Closed Fractional Intersecting Families","publication_year":2023,"publication_date":"2023-12-01","ids":{"openalex":"https://openalex.org/W4389207817","doi":"https://doi.org/10.37236/11651"},"language":"en","primary_location":{"id":"doi:10.37236/11651","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/11651","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p37/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/v30i4p37/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062000960","display_name":"Niranjan Balachandran","orcid":"https://orcid.org/0000-0002-4142-3857"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Niranjan Balachandran","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Bombay, Mumbai"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Bombay, Mumbai","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009284589","display_name":"Srimanta Bhattacharya","orcid":"https://orcid.org/0000-0002-2612-0217"},"institutions":[{"id":"https://openalex.org/I4210113248","display_name":"Indian Institute of Technology Palakkad","ror":"https://ror.org/0264cg909","country_code":"IN","type":"facility","lineage":["https://openalex.org/I4210113248"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Srimanta Bhattacharya","raw_affiliation_strings":["Department of Computer Science and Engineering, Indian Institute of Technology Palakkad, Palakkad"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Indian Institute of Technology Palakkad, Palakkad","institution_ids":["https://openalex.org/I4210113248"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083667458","display_name":"Krishn Vishwas Kher","orcid":null},"institutions":[{"id":"https://openalex.org/I65181880","display_name":"Indian Institute of Technology Hyderabad","ror":"https://ror.org/01j4v3x97","country_code":"IN","type":"education","lineage":["https://openalex.org/I65181880"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Krishn Kher","raw_affiliation_strings":["Department of Engineering Science cum Computer Science and Engineering, Indian Institute of Technology Hyderabad, Hyderabad"],"affiliations":[{"raw_affiliation_string":"Department of Engineering Science cum Computer Science and Engineering, Indian Institute of Technology Hyderabad, Hyderabad","institution_ids":["https://openalex.org/I65181880"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076736694","display_name":"Rogers Mathew","orcid":"https://orcid.org/0000-0003-4536-1136"},"institutions":[{"id":"https://openalex.org/I65181880","display_name":"Indian Institute of Technology Hyderabad","ror":"https://ror.org/01j4v3x97","country_code":"IN","type":"education","lineage":["https://openalex.org/I65181880"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rogers Mathew","raw_affiliation_strings":["Department of Computer Science and Engineering, Indian Institute of Technology Hyderabad, Hyderabad"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Indian Institute of Technology Hyderabad, Hyderabad","institution_ids":["https://openalex.org/I65181880"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103096375","display_name":"Brahadeesh Sankarnarayanan","orcid":"https://orcid.org/0000-0001-9191-1253"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Brahadeesh Sankarnarayanan","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Bombay, Mumbai"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Bombay, Mumbai","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5062000960"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":1.3489,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7825942,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"30","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9945999979972839,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9945999979972839,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9592999815940857,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9564999938011169,"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/combinatorics","display_name":"Combinatorics","score":0.8284816741943359},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7868965864181519},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.6840449571609497},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6680967807769775},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5370340347290039},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.43545791506767273},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37641268968582153},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06933018565177917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06260773539543152}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8284816741943359},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7868965864181519},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.6840449571609497},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6680967807769775},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5370340347290039},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.43545791506767273},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37641268968582153},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06933018565177917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06260773539543152},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"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/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/11651","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/11651","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p37/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:10.37236/11651","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/11651","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p37/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/G6771488830","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"},{"id":"https://openalex.org/G7618479683","display_name":null,"funder_award_id":"MTR/2019/000550","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"},{"id":"https://openalex.org/G7800732931","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"}],"funders":[{"id":"https://openalex.org/F4320323196","display_name":"National Board for Higher Mathematics","ror":"https://ror.org/02m388s04"},{"id":"https://openalex.org/F4320323448","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152"},{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"},{"id":"https://openalex.org/F4320335719","display_name":"Industrial Research and Consultancy Centre","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389207817.pdf"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1981753242","https://openalex.org/W1986908956","https://openalex.org/W2050639196","https://openalex.org/W2064197162","https://openalex.org/W2120888988","https://openalex.org/W3000266334","https://openalex.org/W3016159905","https://openalex.org/W3103491165","https://openalex.org/W3194328708","https://openalex.org/W4288101848","https://openalex.org/W4313898101","https://openalex.org/W4383312127"],"related_works":["https://openalex.org/W4288024920","https://openalex.org/W2987986312","https://openalex.org/W2898780680","https://openalex.org/W2390073374","https://openalex.org/W3119412844","https://openalex.org/W2575225986","https://openalex.org/W4297914395","https://openalex.org/W2025239573","https://openalex.org/W2158905189","https://openalex.org/W4319874546"],"abstract_inverted_index":{"For":[0],"a":[1,9,15,21,101,116,128],"set":[2],"$L$":[3],"of":[4,120],"positive":[5,10],"proper":[6],"fractions":[7],"and":[8,37,78,94,126],"integer":[11],"$r":[12,75],"\\geq":[13,76],"2$,":[14],"fractional":[16,83],"$r$-closed":[17,84,130],"$L$-intersecting":[18],"family":[19,86,132],"is":[20,96,133],"collection":[22],"$\\mathcal{F}":[23],"\\subset":[24],"\\mathcal{P}([n])$":[25],"with":[26],"the":[27,109],"property":[28],"that":[29,49,73,107,127],"for":[30,74],"any":[31,82],"$2":[32],"\\leq":[33,35],"t":[34],"r$":[36],"$A_1,":[38],"\\dotsc,":[39,63],"A_t":[40,55,66],"\\in":[41,46,57],"\\mathcal{F}$":[42],"there":[43],"exists":[44],"$\\theta":[45,111],"L$":[47],"such":[48],"$\\lvert":[50],"A_1":[51,61],"\\cap":[52,54],"\\dotsb":[53],"\\rvert":[56],"\\{":[58],"\\theta":[59,64],"\\lvert":[60,65],"\\rvert,":[62],"\\rvert\\}$.":[67],"In":[68],"this":[69,95],"paper":[70],"we":[71,114],"show":[72,106],"3$":[77],"$L":[79],"=":[80,112],"\\{\\theta\\}$":[81],"$\\theta$-intersecting":[85],"has":[87],"size":[88],"at":[89],"most":[90],"linear":[91],"in":[92,108],"$n$,":[93],"best":[97],"possible":[98],"up":[99,136],"to":[100,137],"constant":[102],"factor.":[103],"We":[104],"also":[105],"case":[110],"1/2$":[113],"have":[115],"tight":[117],"upper":[118],"bound":[119],"$\\lfloor":[121],"\\frac{3n}{2}":[122],"\\rfloor":[123],"-":[124],"2$":[125],"maximal":[129],"$(1/2)$-intersecting":[131],"determined":[134],"uniquely":[135],"isomorphism.":[138]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}