{"id":"https://openalex.org/W2144515537","doi":"https://doi.org/10.37236/591","title":"Chung-Feller Property in View of Generating Functions","display_name":"Chung-Feller Property in View of Generating Functions","publication_year":2011,"publication_date":"2011-05-08","ids":{"openalex":"https://openalex.org/W2144515537","doi":"https://doi.org/10.37236/591","mag":"2144515537"},"language":"en","primary_location":{"id":"doi:10.37236/591","is_oa":true,"landing_page_url":"https://doi.org/10.37236/591","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p104/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":null,"license_id":null,"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/v18i1p104/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020831949","display_name":"Shu-Chung Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Shu-Chung Liu","raw_affiliation_strings":["National Tsing Hua University"],"affiliations":[{"raw_affiliation_string":"National Tsing Hua University","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100365040","display_name":"Yi Wang","orcid":"https://orcid.org/0000-0003-4997-5338"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Wang","raw_affiliation_strings":["Dalian Univ of Tech"],"affiliations":[{"raw_affiliation_string":"Dalian Univ of Tech","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012604019","display_name":"Yeong\u2010Nan Yeh","orcid":"https://orcid.org/0000-0001-8249-3133"},"institutions":[{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yeong-Nan Yeh","raw_affiliation_strings":["Academia Sinica )"],"affiliations":[{"raw_affiliation_string":"Academia Sinica )","institution_ids":["https://openalex.org/I84653119"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020831949"],"corresponding_institution_ids":["https://openalex.org/I25846049"],"apc_list":null,"apc_paid":null,"fwci":0.4481,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.62250623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"18","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":0.9995999932289124,"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":0.9995999932289124,"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":0.9832000136375427,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9700000286102295,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.883743166923523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8598574995994568},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.7278165817260742},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7155354022979736},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7015763521194458},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6975584030151367},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4869929254055023},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.42485445737838745},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0615498423576355},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.05992397665977478}],"concepts":[{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.883743166923523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8598574995994568},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7278165817260742},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7155354022979736},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7015763521194458},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6975584030151367},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4869929254055023},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.42485445737838745},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0615498423576355},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.05992397665977478},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/591","is_oa":true,"landing_page_url":"https://doi.org/10.37236/591","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p104/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.372.8831","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.8831","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/v18i1p104/pdf/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/591","is_oa":true,"landing_page_url":"https://doi.org/10.37236/591","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p104/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2853386864","display_name":null,"funder_award_id":"11071030","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321040","display_name":"National Science Council","ror":"https://ror.org/02kv4zf79"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2144515537.pdf","grobid_xml":"https://content.openalex.org/works/W2144515537.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W200226848","https://openalex.org/W320120465","https://openalex.org/W1492470654","https://openalex.org/W1533235983","https://openalex.org/W1551177513","https://openalex.org/W1607925521","https://openalex.org/W1966578568","https://openalex.org/W1967542071","https://openalex.org/W1977020890","https://openalex.org/W2002148978","https://openalex.org/W2011280299","https://openalex.org/W2014541558","https://openalex.org/W2019731586","https://openalex.org/W2034011690","https://openalex.org/W2037840682","https://openalex.org/W2038250522","https://openalex.org/W2040069491","https://openalex.org/W2040889864","https://openalex.org/W2060752732","https://openalex.org/W2090215490","https://openalex.org/W2113472141","https://openalex.org/W2134788705","https://openalex.org/W2152508360","https://openalex.org/W2330477670","https://openalex.org/W2400686333","https://openalex.org/W2914659449","https://openalex.org/W2992732741","https://openalex.org/W3080542154","https://openalex.org/W4239870290","https://openalex.org/W4247320913","https://openalex.org/W6600146492","https://openalex.org/W6607530787","https://openalex.org/W6805331278"],"related_works":["https://openalex.org/W1991467510","https://openalex.org/W1946545129","https://openalex.org/W3036035571","https://openalex.org/W2920421993","https://openalex.org/W2999782644","https://openalex.org/W4376108057","https://openalex.org/W3011729766","https://openalex.org/W4302428509","https://openalex.org/W2950604330","https://openalex.org/W2064893329"],"abstract_inverted_index":{"The":[0,25,94,172],"classical":[1],"Chung-Feller":[2,71,133],"Theorem":[3],"offers":[4],"an":[5],"elegant":[6],"perspective":[7],"for":[8,143,152],"enumerating":[9],"the":[10,17,22,29,32,48,58,70,84,98,119,141,144,147,153,160],"Catalan":[11],"number":[12],"$c_n=":[13],"\\frac{1}{n+1}\\binom{2n}{n}$.":[14],"One":[15],"of":[16,31,54,60,83,122],"various":[18],"proofs":[19],"is":[20,41,63,87],"by":[21,159],"uniform-partition":[23,99],"method.":[24],"method":[26,100],"shows":[27],"that":[28,81],"set":[30,75],"free":[33,167],"Dyck":[34,50],"$n$-paths,":[35],"which":[36],"have":[37],"$\\binom{2n}{n}$":[38],"in":[39],"total,":[40],"uniformly":[42,78],"partitioned":[43,79],"into":[44],"$n+1$":[45],"blocks,":[46],"and":[47,124,135,146],"ordinary":[49],"$n$-paths":[51],"form":[52],"one":[53,82],"these":[55],"blocks;":[56],"therefore":[57],"cardinality":[59],"each":[61],"block":[62],"$\\frac{1}{n+1}\\binom{2n}{n}$.":[64],"In":[65],"this":[66],"article,":[67],"we":[68,105,127,156],"study":[69],"property:":[72],"a":[73,90,110,115],"sup-structure":[74],"can":[76],"be":[77],"such":[80],"partition":[85],"blocks":[86],"(isomorphic":[88],"to)":[89],"well-known":[91],"structure":[92],"set.":[93],"previous":[95],"works":[96],"about":[97,132],"used":[101],"bijections,":[102],"but":[103],"here":[104],"apply":[106],"generating":[107,120],"functions":[108,121],"as":[109,170],"new":[111,138,161],"approach.":[112],"By":[113],"claiming":[114],"functional":[116],"equation":[117],"involving":[118],"sup-":[123],"sub-structure":[125],"sets,":[126],"re-prove":[128],"two":[129],"known":[130],"results":[131],"property,":[134],"explore":[136],"several":[137],"examples":[139],"including":[140],"ones":[142],"large":[145],"little":[148],"Schr\u00f6der":[149,154,168],"paths.":[150],"Especially":[151],"paths,":[155],"are":[157,175],"led":[158],"approach":[162],"straightforwardly":[163],"to":[164],"consider":[165],"\"weighted\"":[166],"paths":[169],"sup-structures.":[171],"weighted":[173],"structures":[174],"not":[176],"obvious":[177],"via":[178],"bijections":[179],"or":[180],"other":[181],"methods.":[182]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}