{"id":"https://openalex.org/W2170629083","doi":"https://doi.org/10.37236/1602","title":"Six Lonely Runners","display_name":"Six Lonely Runners","publication_year":2001,"publication_date":"2001-02-06","ids":{"openalex":"https://openalex.org/W2170629083","doi":"https://doi.org/10.37236/1602","mag":"2170629083"},"language":"en","primary_location":{"id":"doi:10.37236/1602","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1602","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i2r3/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":false,"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":null,"license_id":null,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i2r3/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079523589","display_name":"Tom Bohman","orcid":"https://orcid.org/0000-0002-4051-2401"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"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","US"],"is_corresponding":true,"raw_author_name":"Tom Bohman","raw_affiliation_strings":["Department of Mathematics Technion -Israel Institute of Technology","Department of Mathematics Massachusetts Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Technion -Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Department of Mathematics Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027529325","display_name":"Ron Holzman","orcid":"https://orcid.org/0000-0002-4629-410X"},"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"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Ron Holzman","raw_affiliation_strings":["Department of Mathematics Massachusetts Institute of Technology","Department of Mathematics Technion -Israel Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics Technion -Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109204552","display_name":"Dan Kleitman","orcid":null},"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"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Dan Kleitman","raw_affiliation_strings":["Department of Mathematics Technion -Israel Institute of Technology","Department of Mathematics Massachusetts Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Technion -Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Department of Mathematics Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5079523589"],"corresponding_institution_ids":["https://openalex.org/I174306211","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.482,"has_fulltext":true,"cited_by_count":39,"citation_normalized_percentile":{"value":0.66258396,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"8","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9869999885559082,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9869999885559082,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9864000082015991,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9836999773979187,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8546847701072693},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8189907073974609},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7561734914779663},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.47101983428001404},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3429066836833954}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8546847701072693},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8189907073974609},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7561734914779663},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.47101983428001404},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3429066836833954}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1602","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1602","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i2r3/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":false,"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":null,"license_id":null,"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:10.37236/1602","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1602","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i2r3/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":false,"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":null,"license_id":null,"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/G6871373857","display_name":"Mathematical Sciences Postdoctoral Research Fellowships","funder_award_id":"9627408","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/F4320309369","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2170629083.pdf","grobid_xml":"https://content.openalex.org/works/W2170629083.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1980792135","https://openalex.org/W1991489592","https://openalex.org/W2004181176","https://openalex.org/W2021456519","https://openalex.org/W2078557945","https://openalex.org/W2081866677","https://openalex.org/W2088648195","https://openalex.org/W2116322414","https://openalex.org/W4232725309","https://openalex.org/W4242981638","https://openalex.org/W4251936773"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2036109498"],"abstract_inverted_index":{"For":[0],"$x$":[1,11],"real,":[2],"let":[3],"$":[4,13,43,48,57,64,66],"\\{x\\}$":[5],"be":[6],"the":[7,27,31],"fractional":[8],"part":[9],"of":[10,30],"(i.e.":[12],"\\{x\\}":[14],"=":[15],"x":[16,19],"-":[17],"\\lfloor":[18],"\\rfloor":[20],"$).":[21],"In":[22],"this":[23],"paper":[24],"we":[25],"prove":[26],"$k=5$":[28],"case":[29],"following":[32],"conjecture":[33],"(the":[34],"lonely":[35],"runner":[36],"conjecture):":[37],"for":[38,65],"any":[39],"$k$":[40],"positive":[41],"reals":[42],"v_1,":[44],"\\dots":[45],",":[46],"v_k":[47],"there":[49],"exists":[50],"a":[51],"real":[52],"number":[53],"$t$":[54],"such":[55],"that":[56],"1/(k+1)":[58],"\\le":[59,62],"\\{v_it":[60],"\\}":[61],"k/(k+1)":[63],"i=":[67],"1,":[68],"\\dots,":[69],"k$.":[70]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2016-06-24T00:00:00"}
