{"id":"https://openalex.org/W2885672736","doi":"https://doi.org/10.1080/00029890.2018.1460977","title":"A short proof of a sum of powers formula","display_name":"A short proof of a sum of powers formula","publication_year":2018,"publication_date":"2018-08-03","ids":{"openalex":"https://openalex.org/W2885672736","doi":"https://doi.org/10.1080/00029890.2018.1460977","mag":"2885672736"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2018.1460977","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1460977","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028025364","display_name":"Enrique Trevi\u00f1o","orcid":"https://orcid.org/0000-0002-7041-9814"},"institutions":[{"id":"https://openalex.org/I162514690","display_name":"Lake Forest College","ror":"https://ror.org/04rmtzr09","country_code":"US","type":"education","lineage":["https://openalex.org/I162514690"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Enrique Trevi\u00f1o","raw_affiliation_strings":["Lake Forest College"],"affiliations":[{"raw_affiliation_string":"Lake Forest College","institution_ids":["https://openalex.org/I162514690"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028025364"],"corresponding_institution_ids":["https://openalex.org/I162514690"],"apc_list":null,"apc_paid":null,"fwci":1.0757,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73144177,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"125","issue":"7","first_page":"659","last_page":"659"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9952999949455261,"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":0.9952999949455261,"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":0.9797999858856201,"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/T12508","display_name":"Functional Equations Stability Results","score":0.960099995136261,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/combinatorial-proof","display_name":"Combinatorial proof","score":0.6479613780975342},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6078041195869446},{"id":"https://openalex.org/keywords/stirling-number","display_name":"Stirling number","score":0.5836182236671448},{"id":"https://openalex.org/keywords/stirling-numbers-of-the-second-kind","display_name":"Stirling numbers of the second kind","score":0.5699201822280884},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5601791143417358},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46816158294677734},{"id":"https://openalex.org/keywords/stirling-numbers-of-the-first-kind","display_name":"Stirling numbers of the first kind","score":0.4470246136188507},{"id":"https://openalex.org/keywords/bell-polynomials","display_name":"Bell polynomials","score":0.42690223455429077},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3978079557418823},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23172220587730408}],"concepts":[{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.6479613780975342},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6078041195869446},{"id":"https://openalex.org/C168902406","wikidata":"https://www.wikidata.org/wiki/Q80918","display_name":"Stirling number","level":2,"score":0.5836182236671448},{"id":"https://openalex.org/C2284495","wikidata":"https://www.wikidata.org/wiki/Q2601117","display_name":"Stirling numbers of the second kind","level":2,"score":0.5699201822280884},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5601791143417358},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46816158294677734},{"id":"https://openalex.org/C93765064","wikidata":"https://www.wikidata.org/wiki/Q2657556","display_name":"Stirling numbers of the first kind","level":3,"score":0.4470246136188507},{"id":"https://openalex.org/C154485487","wikidata":"https://www.wikidata.org/wiki/Q815666","display_name":"Bell polynomials","level":2,"score":0.42690223455429077},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3978079557418823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23172220587730408},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2018.1460977","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1460977","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2055957746"],"related_works":["https://openalex.org/W1515501413","https://openalex.org/W2153676633","https://openalex.org/W2799775110","https://openalex.org/W2081524161","https://openalex.org/W1644555362","https://openalex.org/W3108596636","https://openalex.org/W2162130471","https://openalex.org/W4300547703","https://openalex.org/W2389973687","https://openalex.org/W2597212942"],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2,27],"combinatorial":[3],"proof":[4],"of":[5,16,23,25,29],"the":[6,17,21],"following":[7],"classical":[8],"result:Theorem.":[9],"(1)":[10],"where":[11],",":[12],"denoting":[13],"Stirling":[14],"numbers":[15],"second":[18],"kind,":[19],"is":[20],"number":[22],"ways":[24],"partitioning":[26],"set":[28],"n":[30],"labelled":[31],"objects":[32],"...":[33]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}