{"id":"https://openalex.org/W2922282992","doi":"https://doi.org/10.1080/00029890.2019.1546077","title":"Differences of Bijections","display_name":"Differences of Bijections","publication_year":2019,"publication_date":"2019-03-07","ids":{"openalex":"https://openalex.org/W2922282992","doi":"https://doi.org/10.1080/00029890.2019.1546077","mag":"2922282992"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2019.1546077","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2019.1546077","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/A5070211483","display_name":"Daniel H. Ullman","orcid":null},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniel H. Ullman","raw_affiliation_strings":["Department of Mathematics, The George Washington University, Washington, DC 20052, USA;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The George Washington University, Washington, DC 20052, USA;","institution_ids":["https://openalex.org/I193531525"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009289337","display_name":"Daniel J. Velleman","orcid":"https://orcid.org/0000-0003-4632-1742"},"institutions":[{"id":"https://openalex.org/I111236770","display_name":"University of Vermont","ror":"https://ror.org/0155zta11","country_code":"US","type":"education","lineage":["https://openalex.org/I111236770"]},{"id":"https://openalex.org/I177605424","display_name":"Amherst College","ror":"https://ror.org/028vqfs63","country_code":"US","type":"education","lineage":["https://openalex.org/I177605424"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniel J. Velleman","raw_affiliation_strings":["Department of Mathematics and Statistics, Amherst College, Amherst, MA 01002, USA;","Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05405, USA"],"raw_orcid":"https://orcid.org/0000-0003-4632-1742","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Amherst College, Amherst, MA 01002, USA;","institution_ids":["https://openalex.org/I177605424"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05405, USA","institution_ids":["https://openalex.org/I111236770"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5009289337","https://openalex.org/A5070211483"],"corresponding_institution_ids":["https://openalex.org/I111236770","https://openalex.org/I177605424","https://openalex.org/I193531525"],"apc_list":null,"apc_paid":null,"fwci":0.1168,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.42229517,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"126","issue":"3","first_page":"199","last_page":"216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9987000226974487,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.993523895740509},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.8778588771820068},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.767015278339386},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6266937255859375},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47833749651908875},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3996075391769409},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3515893220901489},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33293619751930237},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32130569219589233},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.08510592579841614}],"concepts":[{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.993523895740509},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8778588771820068},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.767015278339386},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6266937255859375},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47833749651908875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3996075391769409},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3515893220901489},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33293619751930237},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32130569219589233},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.08510592579841614},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2019.1546077","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2019.1546077","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":9,"referenced_works":["https://openalex.org/W1967848384","https://openalex.org/W1974662261","https://openalex.org/W1977834112","https://openalex.org/W2024897051","https://openalex.org/W2072700893","https://openalex.org/W2315761084","https://openalex.org/W2320743697","https://openalex.org/W2329297542","https://openalex.org/W2916718594"],"related_works":["https://openalex.org/W1991467510","https://openalex.org/W2952277453","https://openalex.org/W2952259524","https://openalex.org/W4286233230","https://openalex.org/W1669060173","https://openalex.org/W2160566290","https://openalex.org/W1986815418","https://openalex.org/W3036035571","https://openalex.org/W3196177307","https://openalex.org/W1994661605"],"abstract_inverted_index":{"When":[0],"is":[1],"a":[2,12,25,42,67,88],"function":[3,89],"from":[4],"an":[5],"abelian":[6,39,53],"group":[7,82],"to":[8,91],"itself":[9],"expressible":[10],"as":[11,66],"difference":[13,68],"of":[14,31,45,69,81,87],"two":[15],"bijections?":[16],"Answering":[17],"this":[18],"question":[19,36,50,77],"for":[20,37,51],"finite":[21,38],"cyclic":[22],"groups":[23],"solves":[24],"problem":[26,62],"about":[27,93],"juggling.":[28],"A":[29],"theorem":[30,44],"Marshall":[32],"Hall":[33],"settles":[34,48],"the":[35,49,61,76,79,85],"groups,":[40],"and":[41],"forgotten":[43],"L\u00e1szl\u00f3":[46],"Fuchs":[47],"infinite":[52],"groups.":[54],"After":[55],"explicating":[56],"these":[57],"theorems,":[58],"we":[59],"extend":[60,75],"by":[63],"examining":[64],"expressibility":[65,86],"injections":[70],"or":[71],"surjections.":[72],"We":[73],"also":[74],"beyond":[78],"realm":[80],"theory,":[83],"where":[84],"translates":[90],"questions":[92],"partial":[94],"transversals":[95],"in":[96],"Latin":[97],"squares.":[98]},"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}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
