{"id":"https://openalex.org/W1620865523","doi":"https://doi.org/10.37236/4252","title":"The Number of Moves of the Largest Disc in Shortest Paths on Hanoi Graphs","display_name":"The Number of Moves of the Largest Disc in Shortest Paths on Hanoi Graphs","publication_year":2014,"publication_date":"2014-11-20","ids":{"openalex":"https://openalex.org/W1620865523","doi":"https://doi.org/10.37236/4252","mag":"1620865523"},"language":"en","primary_location":{"id":"doi:10.37236/4252","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4252","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p38/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/v21i4p38/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020984171","display_name":"Simon Aumann","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Simon Aumann","raw_affiliation_strings":["Department of Mathematics\r\nUniversity of Munich","Department of Mathematics#R##N#University of Munich"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics\r\nUniversity of Munich","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics#R##N#University of Munich","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012816753","display_name":"Katharina A.M. G\u00f6tz","orcid":null},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Katharina A.M. G\u00f6tz","raw_affiliation_strings":["German Space Operations Center"],"affiliations":[{"raw_affiliation_string":"German Space Operations Center","institution_ids":["https://openalex.org/I2898391981"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019534469","display_name":"Andr\u00e9as Hinz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andreas M. Hinz","raw_affiliation_strings":["Department of Mathematics\r\nUniversity of Munich\r\nDepartment for Mathematics and Computer Science\r\nUniversity of Maribor","Department of Mathematics#R##N#University of Munich#R##N#Department for Mathematics and Computer Science#R##N#University of Maribor"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics\r\nUniversity of Munich\r\nDepartment for Mathematics and Computer Science\r\nUniversity of Maribor","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics#R##N#University of Munich#R##N#Department for Mathematics and Computer Science#R##N#University of Maribor","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074292682","display_name":"Ciril Petr","orcid":"https://orcid.org/0000-0002-3475-7787"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ciril Petr","raw_affiliation_strings":["Department for Mathematics and Computer Science\r\nUniversity of Maribor","Department for Mathematics and Computer Science#R##N#University of Maribor"],"affiliations":[{"raw_affiliation_string":"Department for Mathematics and Computer Science\r\nUniversity of Maribor","institution_ids":[]},{"raw_affiliation_string":"Department for Mathematics and Computer Science#R##N#University of Maribor","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5020984171"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5371,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.90519071,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"21","issue":"4","first_page":null,"last_page":null},"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/T13664","display_name":"Genome Rearrangement Algorithms","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"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/T11567","display_name":"semigroups and automata theory","score":0.9929999709129333,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7769906520843506},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7463359832763672},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6364865899085999},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.48091360926628113},{"id":"https://openalex.org/keywords/tower","display_name":"Tower","score":0.4202577769756317},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4051853120326996},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.15127593278884888}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7769906520843506},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7463359832763672},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6364865899085999},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.48091360926628113},{"id":"https://openalex.org/C2777831296","wikidata":"https://www.wikidata.org/wiki/Q12518","display_name":"Tower","level":2,"score":0.4202577769756317},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4051853120326996},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.15127593278884888},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C147176958","wikidata":"https://www.wikidata.org/wiki/Q77590","display_name":"Civil engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/4252","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4252","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p38/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"},{"id":"pmh:oai:dk.um.si:IzpisGradiva.php?id=67353","is_oa":true,"landing_page_url":"https://dk.um.si/IzpisGradiva.php?id=67353","pdf_url":null,"source":{"id":"https://openalex.org/S4377196302","display_name":"University of Maribor digital library (University of Maribor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I37696226","host_organization_name":"University of Maribor","host_organization_lineage":["https://openalex.org/I37696226"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics, vol. 21, no. 4, pp. 1-22, 2014.","raw_type":"info:eu-repo/semantics/report"}],"best_oa_location":{"id":"doi:10.37236/4252","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4252","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p38/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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1620865523.pdf","grobid_xml":"https://content.openalex.org/works/W1620865523.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W566104198","https://openalex.org/W1507039213","https://openalex.org/W1603307171","https://openalex.org/W1964946879","https://openalex.org/W1965106165","https://openalex.org/W1974316666","https://openalex.org/W1994665486","https://openalex.org/W2000497834","https://openalex.org/W2001456233","https://openalex.org/W2027013240","https://openalex.org/W2043901149","https://openalex.org/W2062355182","https://openalex.org/W2155595309","https://openalex.org/W2253017756","https://openalex.org/W2295590981","https://openalex.org/W2962750600","https://openalex.org/W3145128584","https://openalex.org/W3215274301","https://openalex.org/W4246219036","https://openalex.org/W4299985734","https://openalex.org/W6638288052"],"related_works":["https://openalex.org/W1989514868","https://openalex.org/W4309419985","https://openalex.org/W2029981401","https://openalex.org/W4212808623","https://openalex.org/W2951982256","https://openalex.org/W4301344670","https://openalex.org/W2740334431","https://openalex.org/W3093722106","https://openalex.org/W2013467167","https://openalex.org/W3123287700"],"abstract_inverted_index":{"In":[0],"contrast":[1],"to":[2,101,159],"the":[3,7,12,18,31,35,54,61,66,79,123,156,181],"widespread":[4],"interest":[5],"in":[6,17,41,45,65,174],"Frame-Stewart":[8],"conjecture":[9],"(FSC)":[10],"about":[11,164],"optimal":[13,132],"number":[14,55,62,80],"of":[15,21,34,37,56,63,68,71,81,88,97,104,131,153,155,162],"moves":[16,84],"classical":[19],"Tower":[20,67],"Hanoi":[22,42,69],"task":[23],"with":[24],"more":[25,47],"than":[26],"three":[27],"pegs,":[28],"this":[29],"is":[30,122],"first":[32],"study":[33],"question":[36],"investigating":[38],"shortest":[39],"paths":[40,133],"graphs":[43],"$H_p^n$":[44],"a":[46,147,160],"general":[48],"setting.":[49],"Here":[50],"$p$":[51],"stands":[52],"for":[53,60,127],"pegs":[57],"and":[58,106,116],"$n$":[59],"discs":[64],"interpretation":[70],"these":[72,89],"graphs.":[73],"The":[74,86,118],"analysis":[75],"depends":[76],"crucially":[77],"on":[78,146,180],"largest":[82],"disc":[83],"(LDMs).":[85],"patterns":[87],"LDMs":[90,136],"will":[91,111],"be":[92,112],"coded":[93],"as":[94],"binary":[95],"strings":[96],"length":[98],"$p-1$":[99,135],"assigned":[100],"each":[102],"pair":[103],"starting":[105],"goal":[107],"states":[108],"individually.":[109],"This":[110],"approached":[113],"both":[114],"analytically":[115],"numerically.":[117],"main":[119],"theoretical":[120],"achievement":[121],"existence,":[124],"at":[125],"least":[126],"all":[128],"$n\\geqslant":[129],"p(p-2)$,":[130],"where":[134],"are":[137],"necessary.":[138],"Numerical":[139],"results,":[140],"obtained":[141],"by":[142,169],"an":[143],"algorithm":[144],"based":[145],"modified":[148],"breadth-first":[149],"search":[150],"making":[151],"use":[152],"symmetries":[154],"graphs,":[157],"lead":[158],"couple":[161],"conjectures":[163],"some":[165,178],"cases":[166],"not":[167],"covered":[168],"our":[170],"ascertained":[171],"results.":[172],"These,":[173],"turn,":[175],"may":[176],"shed":[177],"light":[179],"notoriously":[182],"open":[183],"FSC.":[184]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}