{"id":"https://openalex.org/W2159064170","doi":"https://doi.org/10.37236/1650","title":"Spanning Trees and Function Classes","display_name":"Spanning Trees and Function Classes","publication_year":2002,"publication_date":"2002-08-12","ids":{"openalex":"https://openalex.org/W2159064170","doi":"https://doi.org/10.37236/1650","mag":"2159064170"},"language":"en","primary_location":{"id":"doi:10.37236/1650","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1650","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r34/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r34/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113693516","display_name":"Jeffery B. Remmel","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jeffery B. Remmel","raw_affiliation_strings":["Department of Mathematics U.C.S.D., La Jolla, CA, 92093-0112"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics U.C.S.D., La Jolla, CA, 92093-0112","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081382164","display_name":"S. Gill Williamson","orcid":"https://orcid.org/0000-0001-6596-4781"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Gill Williamson","raw_affiliation_strings":["Department of Computer Science and Engineering U.C.S.D., La Jolla, CA, 92093-0114"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering U.C.S.D., La Jolla, CA, 92093-0114","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113693516"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7379,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.83206522,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"9","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":0.9984999895095825,"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":0.9984999895095825,"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/T11476","display_name":"Graph theory and applications","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9517999887466431,"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-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.9591923952102661},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8541936874389648},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.8530436754226685},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8515731692314148},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.7612780332565308},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47331154346466064},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43048518896102905}],"concepts":[{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.9591923952102661},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8541936874389648},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8530436754226685},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8515731692314148},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.7612780332565308},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47331154346466064},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43048518896102905}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1650","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1650","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r34/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":false,"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:10.1.1.58.1427","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.58.1427","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/Volume_9/PDF/v9i1r34.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.6.2979","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.2979","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/Volume_9/PostScriptfiles/v9i1r34.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1650","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1650","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r34/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":false,"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":[{"id":"https://metadata.un.org/sdg/15","score":0.6600000262260437,"display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2159064170.pdf","grobid_xml":"https://content.openalex.org/works/W2159064170.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1514415888","https://openalex.org/W1999657405","https://openalex.org/W2028122921","https://openalex.org/W2066824935","https://openalex.org/W2113358778","https://openalex.org/W2294305355","https://openalex.org/W2614099084","https://openalex.org/W3133279294","https://openalex.org/W3158027121"],"related_works":["https://openalex.org/W2030171229","https://openalex.org/W1566789756","https://openalex.org/W2052788654","https://openalex.org/W2146998892","https://openalex.org/W2952873647","https://openalex.org/W2531534570","https://openalex.org/W2154568177","https://openalex.org/W2952699113","https://openalex.org/W4299808048","https://openalex.org/W1650584150"],"abstract_inverted_index":{"If":[0,39],"$G=K_n$":[1],"is":[2,41],"the":[3,6,94,115,134],"complete":[4,43],"graph,":[5,45],"classical":[7],"Pr\u00fcffer":[8],"correspondence":[9],"gives":[10],"a":[11,28,34,42,61,71,124,153],"natural":[12,72],"bijection":[13],"between":[14,76],"all":[15,21,25],"spanning":[16,78,96,110],"trees":[17],"of":[18,30,36,63,74,80,86,108,114,126,139,155],"$G$":[19,40],"(i.e.,":[20],"Cayley":[22],"trees)":[23],"and":[24,54,69,83,103],"functions":[26,92,116],"from":[27],"set":[29,35],"$n-2$":[31],"elements":[32],"to":[33,112,117],"$n$":[37],"elements.":[38],"multipartite":[44],"then":[46],"such":[47],"bijections":[48,75],"have":[49],"been":[50],"studied":[51],"by":[52],"E\u011fecio\u011flu":[53],"Remmel.":[55],"In":[56],"this":[57,101],"paper,":[58],"we":[59,104],"define":[60],"class":[62,73],"directed":[64,130],"graphs,":[65],"called":[66],"filtered":[67],"digraphs,":[68],"describe":[70],"oriented":[77,95],"forests":[79,97,111],"these":[81,109],"digraphs":[82],"associated":[84],"classes":[85],"functions.":[87],"We":[88],"derive":[89],"multivariate":[90,141],"generating":[91,142],"for":[93,129],"which":[98,118],"arise":[99],"in":[100,133],"context,":[102],"link":[105],"basic":[106],"properties":[107,113],"they":[119],"correspond.":[120],"This":[121],"approach":[122],"yields":[123],"number":[125,154],"new":[127,156],"results":[128,149],"graphs.":[131],"Moreover,":[132],"undirected":[135],"case,":[136],"various":[137,147],"specializations":[138],"our":[140],"function":[143],"not":[144],"only":[145],"include":[146],"known":[148],"but":[150],"also":[151],"give":[152],"results.":[157]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}