{"id":"https://openalex.org/W2014674842","doi":"https://doi.org/10.1137/050630180","title":"A New Periodicity Lemma","display_name":"A New Periodicity Lemma","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2014674842","doi":"https://doi.org/10.1137/050630180","mag":"2014674842"},"language":"de","primary_location":{"id":"doi:10.1137/050630180","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050630180","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021073628","display_name":"Kangmin Fan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kangmin Fan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021097696","display_name":"Simon J. Puglisi","orcid":"https://orcid.org/0000-0001-7668-7636"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simon J. Puglisi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108477315","display_name":"W.F. Smyth","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"W. F. Smyth","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014748363","display_name":"Andrew Turpin","orcid":"https://orcid.org/0000-0003-2559-8769"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrew Turpin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5021073628"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3577941,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.89274933,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"20","issue":"3","first_page":"656","last_page":"668"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11269","display_name":"Algorithms and Data Compression","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"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/T12029","display_name":"DNA and Biological Computing","score":0.9994999766349792,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/substring","display_name":"Substring","score":0.6320348978042603},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5754892230033875},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5013265609741211},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22300618886947632}],"concepts":[{"id":"https://openalex.org/C182407805","wikidata":"https://www.wikidata.org/wiki/Q2626534","display_name":"Substring","level":3,"score":0.6320348978042603},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5754892230033875},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5013265609741211},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22300618886947632},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/050630180","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050630180","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:alma.61RMIT_INST:11247016900001341","is_oa":false,"landing_page_url":"http://doi.org/10.1137/050630180","pdf_url":null,"source":{"id":"https://openalex.org/S4306402074","display_name":"RMIT Research Repository (RMIT University Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I82951845","host_organization_name":"RMIT University","host_organization_lineage":["https://openalex.org/I82951845"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:jupiter.its.unimelb.edu.au:11343/29380","is_oa":false,"landing_page_url":"http://hdl.handle.net/11343/29380","pdf_url":null,"source":{"id":"https://openalex.org/S4377196259","display_name":"Minerva Access (University of Melbourne)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I165779595","host_organization_name":"The University of Melbourne","host_organization_lineage":["https://openalex.org/I165779595"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1968517468","https://openalex.org/W1973456884","https://openalex.org/W2007378578","https://openalex.org/W2023034313","https://openalex.org/W2024145045","https://openalex.org/W2035314514","https://openalex.org/W2036042874","https://openalex.org/W2067787802","https://openalex.org/W2077770566","https://openalex.org/W2121252285"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049","https://openalex.org/W2271181815"],"abstract_inverted_index":{"Given":[0],"a":[1,6,14,38,68,82,86,213,222,239],"string":[2,47,135,191],"x":[3,12,35,48,66,102,136,192],"=":[4,17,20,32,71],"x[1..n],":[5],"repetition":[7,93],"of":[8,43,62,77,89,94,101,131,149,186,233,242,258],"period":[9,63,95],"p":[10,19,64,96],"in":[11,45,65,133,189,204,244],"is":[13,37,49,67,81,85,137],"substring":[15,69],"u(r)":[16],"x[i..i+rp-1],":[18],"vertical":[21,24,75,110],"bar":[22,73,108],"u":[23,31],"bar,":[25],"r":[26],">=":[27],"2,":[28],"where":[29,79],"neither":[30],"x[i..i+p-1]":[33],"nor":[34],"[i..i+(r+1)p-1]":[36],"repetition.":[39],"The":[40],"maximum":[41,128,183],"number":[42,129,184,230],"repetitions":[44],"any":[46,134,190],"well":[50],"known":[51],"to":[52,251],"be":[53],"Theta(n":[54],"log":[55],"n).":[56],"A":[57],"run":[58],"or":[59,103],"maximal":[60],"periodicity":[61,223],"u(r)t":[70],"x[i..i+rp+vertical":[72],"t":[74,84,109],"bar-1]":[76],"x,":[78],"ur":[80],"repetition,":[83],"proper":[87],"prefix":[88],"u,":[90],"and":[91,115,144,169,231],"no":[92,146],"begins":[97],"at":[98,105],"position":[99,106],"i-1":[100],"ends":[104],"i+rp+vertical":[107],"bar.":[111],"In":[112,209],"2000":[113],"Kolpakov":[114],"Kucherov":[116],"[J.":[117,171],"Discrete":[118],"Algorithms,":[119],"1":[120],"(":[121],"2000),":[122],"pp.":[123,178],"159-186]":[124],"showed":[125,180],"that":[126,161,181,203,225,235],"the":[127,152,182,201,229,256],"rho(n)":[130,162],"runs":[132],"O(n),":[138],"but":[139],"their":[140],"proof":[141],"was":[142],"nonconstructive":[143],"provided":[145],"specific":[147],"constant":[148],"proportionality.":[150],"At":[151],"same":[153],"time,":[154],"they":[155],"presented":[156],"experimental":[157],"data":[158],"strongly":[159],"suggesting":[160],"<":[163,195,207],"n.":[164,208],"Related":[165],"work":[166],"by":[167],"Fraenkel":[168],"Simpson":[170],"Combin.":[172],"Theory":[173],"Ser.":[174],"A.,":[175],"82":[176],"(1998),":[177],"112-120]":[179],"sigma(n)":[185,194,206],"distinct":[187],"squares":[188],"satisfies":[193],"2n,":[196],"while":[197],"experiment":[198],"again":[199],"encourages":[200],"belief":[202],"fact":[205],"this":[210,249],"paper,":[211],"as":[212],"first":[214],"step":[215],"toward":[216],"proving":[217],"these":[218],"conjectures,":[219],"we":[220],"present":[221],"lemma":[224],"establishes":[226],"limitations":[227,254],"on":[228,255],"range":[232,241],"periodicities":[234],"can":[236],"occur":[237],"over":[238],"specified":[240],"positions":[243],"x.":[245],"We":[246],"then":[247],"apply":[248],"result":[250],"specify":[252],"corresponding":[253],"occurrence":[257],"runs.":[259]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}