{"id":"https://openalex.org/W2992319757","doi":"https://doi.org/10.37236/1614","title":"Sumsets of Finite Beatty Sequences","display_name":"Sumsets of Finite Beatty Sequences","publication_year":2000,"publication_date":"2000-08-15","ids":{"openalex":"https://openalex.org/W2992319757","doi":"https://doi.org/10.37236/1614","mag":"2992319757"},"language":"en","primary_location":{"id":"doi:10.37236/1614","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1614","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i2r15/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/v8i2r15/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082706572","display_name":"Jane Pitman","orcid":null},"institutions":[{"id":"https://openalex.org/I5681781","display_name":"University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Jane Pitman","raw_affiliation_strings":["Department of Pure Mathematics, University of Adelaide, Adelaide, SA 5005, AUSTRALIA"],"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, University of Adelaide, Adelaide, SA 5005, AUSTRALIA","institution_ids":["https://openalex.org/I5681781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5082706572"],"corresponding_institution_ids":["https://openalex.org/I5681781"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.38837604,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"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/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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/T10911","display_name":"Chemical Synthesis and Analysis","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13156","display_name":"Historical Linguistics and Language Studies","score":0.965399980545044,"subfield":{"id":"https://openalex.org/subfields/1203","display_name":"Language and Linguistics"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8790230751037598},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8253649473190308},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5848105549812317},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5792748928070068},{"id":"https://openalex.org/keywords/arithmetic-progression","display_name":"Arithmetic progression","score":0.5429101586341858},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4309905171394348},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34859058260917664},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.122479647397995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8790230751037598},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8253649473190308},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5848105549812317},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5792748928070068},{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.5429101586341858},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4309905171394348},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34859058260917664},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.122479647397995},{"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1614","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1614","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i2r15/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.94.5446","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.94.5446","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_8/PDF/v8i2r15.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1614","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1614","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i2r15/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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2992319757.pdf","grobid_xml":"https://content.openalex.org/works/W2992319757.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1508815299","https://openalex.org/W1555768633","https://openalex.org/W1980203985","https://openalex.org/W2023082890","https://openalex.org/W2023847659","https://openalex.org/W2028491857","https://openalex.org/W2090062988","https://openalex.org/W2139337670","https://openalex.org/W4389255187"],"related_works":["https://openalex.org/W2924691597","https://openalex.org/W2953245366","https://openalex.org/W2332815384","https://openalex.org/W1967777504","https://openalex.org/W3168772390","https://openalex.org/W147178145","https://openalex.org/W1554571931","https://openalex.org/W2963711661","https://openalex.org/W4301851751","https://openalex.org/W2142539551"],"abstract_inverted_index":{"An":[0],"investigation":[1],"of":[2,5,47,49,75,77,93],"the":[3,45,50,73],"size":[4],"$S+S$":[6],"for":[7,72],"a":[8],"finite":[9,79,94],"Beatty":[10],"sequence":[11],"$S=(s_i)=(\\lfloor":[12],"i\\alpha+\\gamma":[13],"\\rfloor)$,":[14],"where":[15],"$\\lfloor":[16],"\\hphantom{x}":[17],"\\rfloor$":[18],"denotes":[19],"\"floor\",":[20],"$\\alpha$,":[21],"$\\gamma$":[22],"are":[23],"real":[24],"with":[25],"$\\alpha\\ge":[26],"1$,":[27],"and":[28,33,55,83],"$0\\le":[29],"i":[30],"\\le":[31],"k-1$":[32],"$k\\ge":[34],"3$.":[35],"For":[36],"$\\alpha&gt;2$,":[37],"it":[38],"is":[39,63,70],"shown":[40],"that":[41,57],"$|S+S|$":[42,90],"depends":[43],"on":[44],"number":[46,74],"\"centres\"":[48],"Sturmian":[51,81],"word":[52],"$\\Delta":[53],"S=(s_i-s_{i-1})$,":[54],"hence":[56],"$3(k-1)\\le":[58],"|S+S|\\le":[59],"4k-6$":[60],"if":[61],"$S$":[62],"not":[64],"an":[65],"arithmetic":[66],"progression.":[67],"A":[68],"formula":[69],"obtained":[71],"centres":[76],"certain":[78],"periodic":[80],"words,":[82],"this":[84],"leads":[85],"to":[86],"further":[87],"information":[88],"about":[89],"in":[91],"terms":[92],"nearest":[95],"integer":[96],"continued":[97],"fractions.":[98]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
