{"id":"https://openalex.org/W2904562472","doi":"https://doi.org/10.23638/dmtcs-21-2-3","title":"Enumeration of super-strong Wilf equivalence classes of permutations in the generalized factor order","display_name":"Enumeration of super-strong Wilf equivalence classes of permutations in the generalized factor order","publication_year":2019,"publication_date":"2019-11-11","ids":{"openalex":"https://openalex.org/W2904562472","doi":"https://doi.org/10.23638/dmtcs-21-2-3","mag":"2904562472"},"language":"en","primary_location":{"id":"doi:10.23638/dmtcs-21-2-3","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-2-3","pdf_url":"https://dmtcs.episciences.org/5880/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://dmtcs.episciences.org/5880/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015774309","display_name":"Ioannis Michos","orcid":"https://orcid.org/0000-0003-1590-7740"},"institutions":[{"id":"https://openalex.org/I201118511","display_name":"European University Cyprus","ror":"https://ror.org/04xp48827","country_code":"CY","type":"education","lineage":["https://openalex.org/I201118511"]}],"countries":["CY"],"is_corresponding":false,"raw_author_name":"Ioannis Michos","raw_affiliation_strings":["Department of Computer Science and Engineering , European University Cyprus , Nicosia , Cyprus","Department of Computer Science and Engineering, European University Cyprus, Nicosia, Cyprus"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering , European University Cyprus , Nicosia , Cyprus","institution_ids":["https://openalex.org/I201118511"]},{"raw_affiliation_string":"Department of Computer Science and Engineering, European University Cyprus, Nicosia, Cyprus","institution_ids":["https://openalex.org/I201118511"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032624443","display_name":"Christina Savvidou","orcid":null},"institutions":[{"id":"https://openalex.org/I185852735","display_name":"University of Lancashire","ror":"https://ror.org/010jbqd54","country_code":"GB","type":"education","lineage":["https://openalex.org/I185852735"]},{"id":"https://openalex.org/I34771391","display_name":"University of Cyprus","ror":"https://ror.org/02qjrjx09","country_code":"CY","type":"education","lineage":["https://openalex.org/I34771391"]},{"id":"https://openalex.org/I4210108889","display_name":"University of Central Lancashire Cyprus","ror":"https://ror.org/020ps3a34","country_code":"CY","type":"education","lineage":["https://openalex.org/I185852735","https://openalex.org/I4210108889"]}],"countries":["CY","GB"],"is_corresponding":false,"raw_author_name":"Christina Savvidou","raw_affiliation_strings":["School of Sciences , UCLan Cyprus , Pyla , Cyprus","School of Sciences, UCLan Cyprus, Pyla, Cyprus"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Sciences , UCLan Cyprus , Pyla , Cyprus","institution_ids":["https://openalex.org/I34771391","https://openalex.org/I4210108889"]},{"raw_affiliation_string":"School of Sciences, UCLan Cyprus, Pyla, Cyprus","institution_ids":["https://openalex.org/I185852735"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1015873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"Vol. 21 no. 2, Permutation...","issue":"Permutation Patterns","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"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":0.9993000030517578,"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/enumeration","display_name":"Enumeration","score":0.934086799621582},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7241379618644714},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6245777606964111},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5728684067726135},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.527355968952179},{"id":"https://openalex.org/keywords/factor","display_name":"Factor (programming language)","score":0.4751284420490265},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.340706467628479},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14346134662628174}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.934086799621582},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7241379618644714},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6245777606964111},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5728684067726135},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.527355968952179},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.4751284420490265},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.340706467628479},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14346134662628174},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.23638/dmtcs-21-2-3","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-2-3","pdf_url":"https://dmtcs.episciences.org/5880/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1803.08818","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.08818","pdf_url":"https://arxiv.org/pdf/1803.08818","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2904562472","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1803.08818.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:doaj.org/article:83062c35640d443da3f4da7c418d0b10","is_oa":true,"landing_page_url":"https://doaj.org/article/83062c35640d443da3f4da7c418d0b10","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science, Vol Vol. 21 no. 2, Permutation..., Iss Permutation Patterns (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.23638/dmtcs-21-2-3","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-2-3","pdf_url":"https://dmtcs.episciences.org/5880/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4000000059604645,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2904562472.pdf","grobid_xml":"https://content.openalex.org/works/W2904562472.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1781129492","https://openalex.org/W2101910429","https://openalex.org/W2122654777","https://openalex.org/W2567618548","https://openalex.org/W2604619812","https://openalex.org/W2963548116","https://openalex.org/W3165109979"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W108845024","https://openalex.org/W2406961474","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2952598754","https://openalex.org/W3042106073","https://openalex.org/W2143566611","https://openalex.org/W4251460363","https://openalex.org/W588267724"],"abstract_inverted_index":{"Super-strong":[0],"Wilf":[1,71,84,112],"equivalence":[2,72,85,113,135],"classes":[3,73,136],"of":[4,35,51,55,67,69,90,125,139],"the":[5,16,43,87,123,146],"symmetric":[6],"group":[7],"${\\mathcal":[8,75],"S}_n$":[9],"on":[10],"$n$":[11,141],"letters,":[12],"with":[13,32],"respect":[14],"to":[15,28,109,131],"generalized":[17],"factor":[18],"order,":[19],"were":[20],"shown":[21],"by":[22,45,94,117,150],"Hadjiloucas,":[23],"Michos":[24],"and":[25,86,99,142,155],"Savvidou":[26],"(2018)":[27,101],"be":[29],"in":[30,49,74,122],"bijection":[31],"pyramidal":[33],"sequences":[34],"consecutive":[36],"differences.":[37],"In":[38],"this":[39],"article":[40],"we":[41,61],"enumerate":[42,143],"latter":[44],"giving":[46],"recursive":[47],"formulae":[48],"terms":[50],"a":[52,59,63,80],"two-dimensional":[53],"analogue":[54],"non-interval":[56],"permutations.":[57],"As":[58],"by-product,":[60],"obtain":[62],"recursively":[64],"defined":[65,93],"set":[66],"representatives":[68],"super-strong":[70,83,111],"S}_n$.":[76],"We":[77],"also":[78],"provide":[79],"connection":[81],"between":[82],"geometric":[88],"notion":[89],"shift":[91,126,134],"equivalence---originally":[92],"Fidler,":[95,151],"Glasscock,":[96,152],"Miceli,":[97,153],"Pantone,":[98,154],"Xu":[100,156],"for":[102,114,137],"words---by":[103],"showing":[104],"that":[105],"an":[106],"alternate":[107],"way":[108],"characterize":[110],"permutations":[115,138],"is":[116],"keeping":[118],"only":[119],"rigid":[120],"shifts":[121],"definition":[124],"equivalence.":[127],"This":[128],"allows":[129],"us":[130],"fully":[132],"describe":[133],"size":[140],"them,":[144],"answering":[145],"corresponding":[147],"problem":[148],"posed":[149],"(2018).":[157],"Comment:":[158],"18":[159],"pages,":[160],"5":[161],"tables":[162]},"counts_by_year":[],"updated_date":"2026-08-23T07:36:19.812096","created_date":"2025-10-10T00:00:00"}