{"id":"https://openalex.org/W1872443082","doi":"https://doi.org/10.1142/s1793830915500287","title":"The most unbalanced words 0<sup>q-p</sup>1<sup>p</sup> and majorization","display_name":"The most unbalanced words 0<sup>q-p</sup>1<sup>p</sup> and majorization","publication_year":2015,"publication_date":"2015-06-05","ids":{"openalex":"https://openalex.org/W1872443082","doi":"https://doi.org/10.1142/s1793830915500287","mag":"1872443082"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830915500287","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830915500287","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5059463845","display_name":"Jetro Vesti","orcid":"https://orcid.org/0000-0002-2553-942X"},"institutions":[{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Jetro Vesti","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland","institution_ids":["https://openalex.org/I155660961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5059463845"],"corresponding_institution_ids":["https://openalex.org/I155660961"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.0479109,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"07","issue":"03","first_page":"1550028","last_page":"1550028"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":1.0,"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":1.0,"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/T11130","display_name":"Coding theory and cryptography","score":0.9969000220298767,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9884999990463257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/majorization","display_name":"Majorization","score":0.8151600360870361},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.75003981590271},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.7000914812088013},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6459061503410339},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6299551725387573},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.6137415170669556},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.5386173129081726},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46736618876457214},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.4621271789073944},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4151632785797119},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3529985845088959},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15018755197525024},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13918271660804749},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11475536227226257},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08073338866233826}],"concepts":[{"id":"https://openalex.org/C2777818330","wikidata":"https://www.wikidata.org/wiki/Q1994695","display_name":"Majorization","level":2,"score":0.8151600360870361},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.75003981590271},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.7000914812088013},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6459061503410339},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6299551725387573},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.6137415170669556},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.5386173129081726},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46736618876457214},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.4621271789073944},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4151632785797119},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3529985845088959},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15018755197525024},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13918271660804749},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11475536227226257},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08073338866233826},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political 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},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830915500287","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830915500287","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1586417893","https://openalex.org/W2023716803","https://openalex.org/W2111591470","https://openalex.org/W2317201179","https://openalex.org/W2330548796"],"related_works":["https://openalex.org/W371413493","https://openalex.org/W1988514170","https://openalex.org/W4320039931","https://openalex.org/W4214702501","https://openalex.org/W2050374035","https://openalex.org/W2524413221","https://openalex.org/W4313303878","https://openalex.org/W1932856329","https://openalex.org/W2247347719","https://openalex.org/W2963815161"],"abstract_inverted_index":{"A":[0],"finite":[1,37,78],"word":[2,96,127,133,185],"w":[3,22],"\u2208":[4],"{0,":[5],"1}*":[6],"is":[7,97,128,134,192,219],"balanced":[8,50,79,95,153],"if":[9],"for":[10],"every":[11,18],"equal-length":[12],"factors":[13],"u":[14,186,218],"and":[15,44,64,81,206],"v":[16],"of":[17,21,36,49,84,93,104,118,125,172,183,199,226],"cyclic":[19],"shift":[20],"we":[23],"have":[24,146],"||u|":[25],"1":[26,29,144,190],"-":[27],"|v|":[28],"|":[30],"\u2264":[31],"1.":[32],"This":[33,167],"new":[34],"class":[35],"words":[38,51,63,80,141,162],"was":[39,73,88,112],"defined":[40],"in":[41,101,121,196,223],"[O.":[42,60],"Jenkinson":[43],"L.":[45],"Q.":[46],"Zamboni,":[47],"Characterisations":[48],"via":[52],"orderings,":[53],"Theoret.":[54],"Comput.":[55],"Sci.310(1\u20133)":[56],"(2004)":[57],"247\u2013271].":[58],"In":[59],"Jenkinson,":[61],"Balanced":[62],"majorization,":[65],"Discrete":[66],"Math.":[67],"Algorithms":[68],"Appl.1(4)":[69],"(2009)":[70],"463\u2013484],":[71],"there":[72],"proved":[74,114],"several":[75],"results":[76,87,174],"considering":[77],"majorization.":[82],"One":[83],"the":[85,90,94,98,102,116,119,122,132,140,152,163,170,173,181,184,193,197,210,220,224],"main":[86],"that":[89,115,139,180,207,217],"base-2":[91,123],"orbit":[92,124,182],"least":[99],"element":[100,195,222],"set":[103,198,225],"orbits":[105,200,227],"with":[106,201,228],"respect":[107,202,229],"to":[108,151,159,203,230],"partial":[109,204,231],"sum.":[110],"It":[111,136],"also":[113,215],"product":[117],"elements":[120],"a":[126],"maximized":[129],"precisely":[130],"when":[131],"balanced.":[135],"turns":[137],"out":[138],"0":[142,188],"q-p":[143,189],"p":[145,191],"similar":[147],"extremal":[148],"properties,":[149],"opposite":[150],"words,":[154],"which":[155],"makes":[156],"it":[157,208],"meaningful":[158],"call":[160],"these":[161],"most":[164],"unbalanced":[165],"words.":[166],"paper":[168],"contains":[169],"counterparts":[171],"mentioned":[175],"above.":[176],"We":[177,213],"will":[178,214],"prove":[179,216],"=":[187],"greatest":[194,221],"sum":[205],"has":[209],"smallest":[211],"product.":[212,232]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}