{"id":"https://openalex.org/W4200475978","doi":"https://doi.org/10.30538/oms2021.0171","title":"Reachability results in labelled \\(t\\)-ary trees","display_name":"Reachability results in labelled \\(t\\)-ary trees","publication_year":2021,"publication_date":"2021-12-18","ids":{"openalex":"https://openalex.org/W4200475978","doi":"https://doi.org/10.30538/oms2021.0171"},"language":"en","primary_location":{"id":"doi:10.30538/oms2021.0171","doi":"https://doi.org/10.30538/oms2021.0171","is_oa":true,"landing_page_url":"https://doi.org/10.30538/oms2021.0171","pdf_url":null,"source":{"id":"https://openalex.org/S4210218690","display_name":"Open Journal of Mathematical Sciences","issn_l":"2523-0212","issn":["2523-0212","2616-4906"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Journal of Mathematical Sciences","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.30538/oms2021.0171","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073222886","display_name":"Isaac Owino Okoth","orcid":"https://orcid.org/0000-0003-4503-4733","observed_orcids":["https://orcid.org/0000-0003-4503-4733"]},"institutions":[{"id":"https://openalex.org/I195610458","display_name":"Maseno University","ror":"https://ror.org/023pskh72","country_code":"KE","type":"education","lineage":["https://openalex.org/I195610458"]}],"countries":["KE"],"is_corresponding":true,"raw_author_name":"Isaac Owino Okoth","raw_affiliation_strings":["Department of Pure and Applied Mathematics, Maseno University, Kenya"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure and Applied Mathematics, Maseno University, Kenya","institution_ids":["https://openalex.org/I195610458"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002587317","display_name":"Albert Oloo Nyariaro","orcid":"https://orcid.org/0000-0002-2997-0241","observed_orcids":["https://orcid.org/0000-0002-2997-0241"]},"institutions":[{"id":"https://openalex.org/I195610458","display_name":"Maseno University","ror":"https://ror.org/023pskh72","country_code":"KE","type":"education","lineage":["https://openalex.org/I195610458"]}],"countries":["KE"],"is_corresponding":false,"raw_author_name":"Albert Oloo Nyariaro","raw_affiliation_strings":["Department of Pure and Applied Mathematics, Maseno University, Kenya"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure and Applied Mathematics, Maseno University, Kenya","institution_ids":["https://openalex.org/I195610458"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073222886"],"corresponding_institution_ids":["https://openalex.org/I195610458"],"apc_list":null,"apc_paid":null,"fwci":0.8159,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.61782236,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":93},"biblio":{"volume":"5","issue":"1","first_page":"360","last_page":"370"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":1.0,"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":1.0,"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":0.0,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.0,"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/path-length","display_name":"path length","score":0.6520000100135803},{"id":"https://openalex.org/keywords/reachability","display_name":"reachability","score":0.9079999923706055},{"id":"https://openalex.org/keywords/enumeration-formulas","display_name":"enumeration formulas","score":0.5889999866485596},{"id":"https://openalex.org/keywords/random-trees","display_name":"random trees","score":0.6740000247955322},{"id":"https://openalex.org/keywords/oriented-trees","display_name":"oriented trees","score":0.42899999022483826}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.8292744159698486},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.7951692342758179},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7636685371398926},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7234487533569336},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6559997797012329},{"id":"https://openalex.org/C143050476","wikidata":"https://www.wikidata.org/wiki/Q194502","display_name":"Sink (geography)","level":2,"score":0.4666367173194885},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4376010000705719},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.4342016875743866},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4037066698074341},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18906885385513306},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10867813229560852},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0},{"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/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.30538/oms2021.0171","doi":"https://doi.org/10.30538/oms2021.0171","is_oa":true,"landing_page_url":"https://doi.org/10.30538/oms2021.0171","pdf_url":null,"source":{"id":"https://openalex.org/S4210218690","display_name":"Open Journal of Mathematical Sciences","issn_l":"2523-0212","issn":["2523-0212","2616-4906"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Journal of Mathematical Sciences","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.30538/oms2021.0171","doi":"https://doi.org/10.30538/oms2021.0171","is_oa":true,"landing_page_url":"https://doi.org/10.30538/oms2021.0171","pdf_url":null,"source":{"id":"https://openalex.org/S4210218690","display_name":"Open Journal of Mathematical Sciences","issn_l":"2523-0212","issn":["2523-0212","2616-4906"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Journal of Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2014305320","https://openalex.org/W2138659323","https://openalex.org/W4299490515","https://openalex.org/W6844488333"],"related_works":["https://openalex.org/W4388442132","https://openalex.org/W3177110514","https://openalex.org/W4282033972","https://openalex.org/W2138659323","https://openalex.org/W2387991068","https://openalex.org/W599250420","https://openalex.org/W1995700396","https://openalex.org/W2782853521","https://openalex.org/W2031347916","https://openalex.org/W2014305320"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,40],"prove":[4],"some":[5],"new":[6],"formulas":[7,43],"in":[8,53],"the":[9,45,85],"enumeration":[10],"of":[11,28,34,47,58,88],"labelled":[12],"\\(t\\)-ary":[13,48,97],"trees":[14,20,49],"by":[15],"path":[16],"lengths.":[17],"We":[18],"treat":[19],"having":[21],"their":[22],"edges":[23],"oriented":[24],"from":[25],"a":[26,32,63,71],"vertex":[27,33],"lower":[29],"label":[30,66],"towards":[31],"higher":[35],"label.":[36],"Among":[37],"other":[38],"results,":[39],"obtain":[41],"counting":[42],"for":[44,94],"number":[46,87],"on":[50],"\\(n\\)":[51],"vertices":[52,91],"which":[54],"there":[55],"are":[56],"paths":[57],"length":[59],"\\(\\ell\\)":[60],"starting":[61],"at":[62,70],"root":[64],"with":[65],"\\(i\\)":[67],"and":[68,80],"ending":[69],"vertex,":[72],"sink,":[73,75],"leaf":[74],"first":[76],"child,":[77],"non-first":[78],"child":[79],"non-leaf.":[81],"For":[82],"each":[83],"statistic,":[84],"average":[86],"these":[89],"reachable":[90],"is":[92],"obtained":[93],"any":[95],"random":[96],"tree.":[98]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2021-12-31T00:00:00"}