{"id":"https://openalex.org/W2584521795","doi":"https://doi.org/10.37236/6411","title":"A New Bijective Proof of Babson and Steingr\u00edmsson's Conjecture","display_name":"A New Bijective Proof of Babson and Steingr\u00edmsson's Conjecture","publication_year":2017,"publication_date":"2017-04-13","ids":{"openalex":"https://openalex.org/W2584521795","doi":"https://doi.org/10.37236/6411","mag":"2584521795"},"language":"en","primary_location":{"id":"doi:10.37236/6411","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6411","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/10.37236/6411","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051173208","display_name":"Joanna N. Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Joanna N. Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5083925869","display_name":"Shouxiao Li","orcid":"https://orcid.org/0000-0003-3886-3840"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shouxiao Li","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051173208"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5035,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.87820288,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"24","issue":"2","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":0.9983000159263611,"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":0.9983000159263611,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11567","display_name":"semigroups and automata theory","score":0.951200008392334,"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/bijection","display_name":"Bijection","score":0.9387385845184326},{"id":"https://openalex.org/keywords/equidistributed-sequence","display_name":"Equidistributed sequence","score":0.8954918384552002},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8487788438796997},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8344177007675171},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7446401715278625},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6961314082145691},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5917806029319763},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.5323451161384583},{"id":"https://openalex.org/keywords/maple","display_name":"Maple","score":0.49563419818878174},{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.4822190999984741},{"id":"https://openalex.org/keywords/statistic","display_name":"Statistic","score":0.4584360718727112},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3273129463195801},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1416296660900116}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.9387385845184326},{"id":"https://openalex.org/C50742451","wikidata":"https://www.wikidata.org/wiki/Q1530388","display_name":"Equidistributed sequence","level":2,"score":0.8954918384552002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8487788438796997},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8344177007675171},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7446401715278625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6961314082145691},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5917806029319763},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.5323451161384583},{"id":"https://openalex.org/C2780414537","wikidata":"https://www.wikidata.org/wiki/Q42292","display_name":"Maple","level":2,"score":0.49563419818878174},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.4822190999984741},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.4584360718727112},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3273129463195801},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1416296660900116},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/6411","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6411","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"}],"best_oa_location":{"id":"doi:10.37236/6411","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6411","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2952259524","https://openalex.org/W2160566290","https://openalex.org/W2806276129","https://openalex.org/W4299611798","https://openalex.org/W2963449060","https://openalex.org/W2021895108","https://openalex.org/W4213409680","https://openalex.org/W2153752510","https://openalex.org/W2949947309","https://openalex.org/W2602388795"],"abstract_inverted_index":{"Babson":[0,65],"and":[1,7,57,66,71,78,87,91],"Steingr\u00edmsson":[2,67],"introduced":[3],"generalized":[4,25,38],"permutation":[5,47],"patterns":[6],"showed":[8],"that":[9,69],"most":[10],"of":[11,24,37,55,63,99,102,114],"the":[12,16,22,52,60],"Mahonian":[13,33],"statistics":[14],"in":[15,35],"literature":[17],"can":[18],"be":[19],"expressed":[20],"by":[21],"combination":[23],"pattern":[26,39],"functions.":[27],"Particularly,":[28],"they":[29],"defined":[30],"a":[31,46,96,100,110],"new":[32,111],"statistic":[34],"terms":[36],"functions,":[40],"which":[41],"is":[42],"denoted":[43],"$stat$.":[44],"Given":[45],"$\\pi$,":[48],"let":[49],"$des(\\pi)$":[50],"denote":[51,59],"descent":[53],"number":[54],"$\\pi$":[56],"$maj(\\pi)$":[58],"major":[61],"index":[62],"$\\pi$.":[64],"conjectured":[68],"$(des,stat)$":[70],"$(des,maj)$":[72],"are":[73],"equidistributed":[74],"on":[75],"$S_n$.":[76],"Foata":[77],"Zeilberger":[79],"settled":[80],"this":[81,103,106,115],"conjecture":[82],"using":[83],"q-enumeration,":[84],"generating":[85],"functions":[86],"Maple":[88],"packages":[89],"ROTA":[90],"PERCY.":[92],"Later,":[93],"Burstein":[94],"provided":[95],"bijective":[97,112],"proof":[98,113],"refinement":[101],"conjecture.":[104,116],"In":[105],"paper,":[107],"we":[108],"give":[109]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}