{"id":"https://openalex.org/W2590778877","doi":"https://doi.org/10.37236/6545","title":"Inversion Generating Functions for Signed Pattern Avoiding Permutations","display_name":"Inversion Generating Functions for Signed Pattern Avoiding Permutations","publication_year":2017,"publication_date":"2017-02-17","ids":{"openalex":"https://openalex.org/W2590778877","doi":"https://doi.org/10.37236/6545","mag":"2590778877"},"language":"en","primary_location":{"id":"doi:10.37236/6545","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6545","pdf_url":null,"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://doi.org/10.37236/6545","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075842748","display_name":"Naiomi T. Cameron","orcid":"https://orcid.org/0000-0001-6848-6615"},"institutions":[{"id":"https://openalex.org/I74201987","display_name":"Lewis & Clark College","ror":"https://ror.org/013pz1582","country_code":"US","type":"education","lineage":["https://openalex.org/I74201987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Naiomi T. Cameron","raw_affiliation_strings":["Lewis & Clark College"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lewis & Clark College","institution_ids":["https://openalex.org/I74201987"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080635755","display_name":"Kendra Killpatrick","orcid":"https://orcid.org/0000-0002-9608-5605"},"institutions":[{"id":"https://openalex.org/I100191712","display_name":"Pepperdine University","ror":"https://ror.org/0529ybh43","country_code":"US","type":"education","lineage":["https://openalex.org/I100191712"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kendra Killpatrick","raw_affiliation_strings":["Pepperdine University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Pepperdine University","institution_ids":["https://openalex.org/I100191712"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09954434,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"1","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":0.9876000285148621,"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":0.9876000285148621,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9495000243186951,"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":0.9138000011444092,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.8454678058624268},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7803533673286438},{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.7194682955741882},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6990054845809937},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.46122413873672485},{"id":"https://openalex.org/keywords/bar","display_name":"Bar (unit)","score":0.41683489084243774},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.33500808477401733},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.24311718344688416},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18806183338165283},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.061987876892089844},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05540856719017029}],"concepts":[{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.8454678058624268},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7803533673286438},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.7194682955741882},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6990054845809937},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.46122413873672485},{"id":"https://openalex.org/C188721877","wikidata":"https://www.wikidata.org/wiki/Q103510","display_name":"Bar (unit)","level":2,"score":0.41683489084243774},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33500808477401733},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.24311718344688416},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18806183338165283},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.061987876892089844},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05540856719017029},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/6545","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6545","pdf_url":null,"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:digitalcommons.pepperdine.edu:faculty_pubs-1101","is_oa":false,"landing_page_url":"https://digitalcommons.pepperdine.edu/faculty_pubs/102","pdf_url":null,"source":{"id":"https://openalex.org/S4377196557","display_name":"Pepperdine Digital Commons (Pepperdine University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I100191712","host_organization_name":"Pepperdine University","host_organization_lineage":["https://openalex.org/I100191712"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"All Faculty Open Access Publications","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/6545","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6545","pdf_url":null,"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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1991467510","https://openalex.org/W2952277453","https://openalex.org/W2952259524","https://openalex.org/W3036035571","https://openalex.org/W2920421993","https://openalex.org/W2999782644","https://openalex.org/W4376108057","https://openalex.org/W4302428509","https://openalex.org/W2950604330","https://openalex.org/W136513132"],"abstract_inverted_index":{"We":[0,74],"consider":[1],"the":[2,7,14,38,43,105,111,120,140],"classical":[3],"Mahonian":[4],"statistics":[5],"on":[6,114,123],"set":[8,28],"$B_n(\\Sigma)$":[9,41,85,145],"of":[10,29,31,40,53,79,107,134],"signed":[11,108],"permutations":[12,109],"in":[13,22,42,65,88,104],"hyperoctahedral":[15],"group":[16],"$B_n$":[17],"which":[18],"avoid":[19],"all":[20,69,148],"patterns":[21,30,52],"$\\Sigma$,":[23],"where":[24,45,71,91],"$\\Sigma$":[25,46,150],"is":[26,60,137],"a":[27,101],"length":[32,54],"two.":[33],"In":[34,93],"2000,":[35],"Simion":[36,80],"gave":[37],"cardinality":[39],"cases":[44,90],"contains":[47],"either":[48],"one":[49],"or":[50],"two":[51,55],"and":[56,117,129],"showed":[57],"that":[58],"$\\left|B_n(\\Sigma)\\right|$":[59],"constant":[61],"whenever":[62],"$\\left|\\Sigma\\right|=1$,":[63],"whereas":[64],"most":[66],"but":[67],"not":[68],"instances":[70],"$\\left|\\Sigma\\right|=2$,":[72],"$\\left|B_n(\\Sigma)\\right|=(n+1)!$.":[73,92],"answer":[75],"an":[76],"open":[77],"question":[78],"by":[81,99,118],"providing":[82,100],"bijections":[83],"from":[84],"to":[86,138],"$S_{n+1}$":[87],"these":[89],"addition,":[94],"we":[95],"extend":[96],"Simion's":[97],"work":[98],"combinatorial":[102],"proof":[103],"language":[106],"for":[110,125,144,146],"major":[112,121],"index":[113,122],"$B_n(21,":[115],"\\bar{2}\\bar{1})$":[116],"giving":[119],"$D_n(\\Sigma)$":[124],"$\\Sigma":[126],"=\\{21,":[127],"\\bar{2}\\bar{1}\\}$":[128],"$\\Sigma=\\{12,21\\}$.":[130],"The":[131],"main":[132],"result":[133],"this":[135],"paper":[136],"give":[139],"inversion":[141],"generating":[142],"functions":[143],"almost":[147],"sets":[149],"with":[151],"$\\left|\\Sigma\\right|\\leq2.$":[152]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}