{"id":"https://openalex.org/W3115943440","doi":"https://doi.org/10.1137/20m1377394","title":"On a Combinatorial Generation Problem of Knuth","display_name":"On a Combinatorial Generation Problem of Knuth","publication_year":2022,"publication_date":"2022-05-05","ids":{"openalex":"https://openalex.org/W3115943440","doi":"https://doi.org/10.1137/20m1377394","mag":"3115943440"},"language":"en","primary_location":{"id":"doi:10.1137/20m1377394","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1377394","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5054178217","display_name":"Arturo Merino","orcid":"https://orcid.org/0000-0002-1728-6936"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]},{"id":"https://openalex.org/I2800345347","display_name":"Berlin Mathematical School","ror":"https://ror.org/03zekj455","country_code":"DE","type":"education","lineage":["https://openalex.org/I2800345347"]},{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]},{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["CZ","DE","GB"],"is_corresponding":true,"raw_author_name":"Arturo Merino","raw_affiliation_strings":["University of Warwick, United Kingdom & Department of Theoretical Computer Science and Mathematical Logic,","( Arturo Merino) Department of Mathematics, TU Berlin, Germany (Ond\u0159ej Mi\u010dka) Department of Theoretical Computer Science and Mathematical Logic,","Charles University, Prague, Czech Republic","Charles University, Prague, Czech Republic (Torsten M\u00fctze) Department of Computer Science,"],"affiliations":[{"raw_affiliation_string":"University of Warwick, United Kingdom & Department of Theoretical Computer Science and Mathematical Logic,","institution_ids":["https://openalex.org/I39555362"]},{"raw_affiliation_string":"( Arturo Merino) Department of Mathematics, TU Berlin, Germany (Ond\u0159ej Mi\u010dka) Department of Theoretical Computer Science and Mathematical Logic,","institution_ids":["https://openalex.org/I2800345347","https://openalex.org/I4577782"]},{"raw_affiliation_string":"Charles University, Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"Charles University, Prague, Czech Republic (Torsten M\u00fctze) Department of Computer Science,","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052402543","display_name":"Ond\u0159ej Mi\u010dka","orcid":"https://orcid.org/0000-0003-3143-4955"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]},{"id":"https://openalex.org/I2800345347","display_name":"Berlin Mathematical School","ror":"https://ror.org/03zekj455","country_code":"DE","type":"education","lineage":["https://openalex.org/I2800345347"]},{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]},{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["CZ","DE","GB"],"is_corresponding":false,"raw_author_name":"Ond\u0159ej Mi\u010dka","raw_affiliation_strings":["Charles University, Prague, Czech Republic","( Arturo Merino) Department of Mathematics, TU Berlin, Germany (Ond\u0159ej Mi\u010dka) Department of Theoretical Computer Science and Mathematical Logic,","Charles University, Prague, Czech Republic (Torsten M\u00fctze) Department of Computer Science,","University of Warwick, United Kingdom & Department of Theoretical Computer Science and Mathematical Logic,"],"affiliations":[{"raw_affiliation_string":"Charles University, Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"( Arturo Merino) Department of Mathematics, TU Berlin, Germany (Ond\u0159ej Mi\u010dka) Department of Theoretical Computer Science and Mathematical Logic,","institution_ids":["https://openalex.org/I2800345347","https://openalex.org/I4577782"]},{"raw_affiliation_string":"Charles University, Prague, Czech Republic (Torsten M\u00fctze) Department of Computer Science,","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"University of Warwick, United Kingdom & Department of Theoretical Computer Science and Mathematical Logic,","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028248747","display_name":"Torsten M\u00fctze","orcid":"https://orcid.org/0000-0002-6383-7436"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]},{"id":"https://openalex.org/I2800345347","display_name":"Berlin Mathematical School","ror":"https://ror.org/03zekj455","country_code":"DE","type":"education","lineage":["https://openalex.org/I2800345347"]},{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]},{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["CZ","DE","GB"],"is_corresponding":false,"raw_author_name":"Torsten M\u00fctze","raw_affiliation_strings":["University of Warwick, United Kingdom & Department of Theoretical Computer Science and Mathematical Logic,","( Arturo Merino) Department of Mathematics, TU Berlin, Germany (Ond\u0159ej Mi\u010dka) Department of Theoretical Computer Science and Mathematical Logic,","Charles University, Prague, Czech Republic","Charles University, Prague, Czech Republic (Torsten M\u00fctze) Department of Computer Science,"],"affiliations":[{"raw_affiliation_string":"University of Warwick, United Kingdom & Department of Theoretical Computer Science and Mathematical Logic,","institution_ids":["https://openalex.org/I39555362"]},{"raw_affiliation_string":"( Arturo Merino) Department of Mathematics, TU Berlin, Germany (Ond\u0159ej Mi\u010dka) Department of Theoretical Computer Science and Mathematical Logic,","institution_ids":["https://openalex.org/I2800345347","https://openalex.org/I4577782"]},{"raw_affiliation_string":"Charles University, Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"Charles University, Prague, Czech Republic (Torsten M\u00fctze) Department of Computer Science,","institution_ids":["https://openalex.org/I21250087"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054178217"],"corresponding_institution_ids":["https://openalex.org/I21250087","https://openalex.org/I2800345347","https://openalex.org/I39555362","https://openalex.org/I4577782"],"apc_list":null,"apc_paid":null,"fwci":0.6897,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73629412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"51","issue":"3","first_page":"379","last_page":"423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9980999827384949,"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":0.9972000122070312,"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/combinatorics","display_name":"Combinatorics","score":0.8306781053543091},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8229894042015076},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7763148546218872},{"id":"https://openalex.org/keywords/coprime-integers","display_name":"Coprime integers","score":0.6691807508468628},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6585976481437683},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5620640516281128},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5488902926445007},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5433384776115417},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.49491995573043823},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45674318075180054},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.42225825786590576},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.22748643159866333},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12065243721008301}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8306781053543091},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8229894042015076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7763148546218872},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.6691807508468628},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6585976481437683},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5620640516281128},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5488902926445007},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5433384776115417},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.49491995573043823},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45674318075180054},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.42225825786590576},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.22748643159866333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12065243721008301},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/20m1377394","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1377394","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:160574","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5859448658","display_name":null,"funder_award_id":"GA 19-08554S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W649265788","https://openalex.org/W1583325710","https://openalex.org/W1625314613","https://openalex.org/W1656699529","https://openalex.org/W1968184858","https://openalex.org/W1971930515","https://openalex.org/W1972094496","https://openalex.org/W1972816631","https://openalex.org/W1978453841","https://openalex.org/W1982120981","https://openalex.org/W1990287270","https://openalex.org/W1995300673","https://openalex.org/W2016348586","https://openalex.org/W2016863833","https://openalex.org/W2023800056","https://openalex.org/W2027483825","https://openalex.org/W2029196217","https://openalex.org/W2044338030","https://openalex.org/W2046815858","https://openalex.org/W2052298978","https://openalex.org/W2057436596","https://openalex.org/W2068462604","https://openalex.org/W2084858300","https://openalex.org/W2086446504","https://openalex.org/W2089687380","https://openalex.org/W2091923122","https://openalex.org/W2097603218","https://openalex.org/W2114138894","https://openalex.org/W2161164856","https://openalex.org/W2166532439","https://openalex.org/W2752061190","https://openalex.org/W2767495301","https://openalex.org/W2963304363","https://openalex.org/W2982014679","https://openalex.org/W3100954633"],"related_works":["https://openalex.org/W3025068760","https://openalex.org/W2177966018","https://openalex.org/W2964242841","https://openalex.org/W4302423208","https://openalex.org/W4363677397","https://openalex.org/W2196131019","https://openalex.org/W2112041331","https://openalex.org/W3164481304","https://openalex.org/W3087194925","https://openalex.org/W3180944311"],"abstract_inverted_index":{"The":[0],"well-known":[1],"middle":[2],"levels":[3],"conjecture":[4,71,131],"asserts":[5],"that":[6,35,79,144],"for":[7,138],"every":[8],"integer":[9],"n":[10,23],"\u2265":[11,142],"1,":[12],"all":[13],"binary":[14],"strings":[15,39],"of":[16,59,69,82,94,103],"length":[17],"2(n":[18],"+":[19,24,100,119,149],"1)":[20,120],"with":[21,46,84],"exactly":[22],"1":[25,101,116,143],"many":[26],"0s":[27],"and":[28,107],"1s":[29],"can":[30],"be":[31],"ordered":[32],"cyclically":[33],"so":[34],"any":[36],"two":[37],"consecutive":[38],"differ":[40],"in":[41,74,91,132,164,170],"swapping":[42],"the":[43,80,86,104,122],"first":[44,87],"bit":[45,49,88],"a":[47,66,133],"complementary":[48],"at":[50],"some":[51],"later":[52],"position.":[53],"In":[54,125],"his":[55],"book":[56],"\u2018The":[57],"Art":[58],"Computer":[60],"Programming":[61],"Vol.":[62],"4A\u2019":[63],"Knuth":[64],"raised":[65],"stronger":[67],"form":[68],"this":[70,126,158],"(Problem":[72],"56":[73],"Section":[75],"7.2.1.3),":[76],"which":[77,85],"requires":[78],"sequence":[81],"positions":[83],"is":[89,110],"swapped":[90],"each":[92,108,161],"step":[93],"such":[95],"an":[96,154],"ordering":[97],"has":[98],"2n":[99,118,148],"blocks":[102],"same":[105],"length,":[106],"block":[109],"obtained":[111],"by":[112],"adding":[113],"s":[114,141],"=":[115],"(modulo":[117],"to":[121,147,156],"previous":[123],"block.":[124],"work,":[127],"we":[128],"prove":[129],"Knuth's":[130],"more":[134],"general":[135],"form,":[136],"allowing":[137],"arbitrary":[139],"shifts":[140],"are":[145],"coprime":[146],"1.":[150],"We":[151],"also":[152],"present":[153],"algorithm":[155],"compute":[157],"ordering,":[159],"generating":[160],"new":[162],"bitstring":[163],"(n)":[165,168],"time,":[166],"using":[167],"memory":[169],"total.
\\n
\\n
\\n":[171]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2021-01-05T00:00:00"}