{"id":"https://openalex.org/W4411150346","doi":"https://doi.org/10.1080/00029890.2025.2500895","title":"Triangle Inequalities Indexed by Graphs","display_name":"Triangle Inequalities Indexed by Graphs","publication_year":2025,"publication_date":"2025-06-09","ids":{"openalex":"https://openalex.org/W4411150346","doi":"https://doi.org/10.1080/00029890.2025.2500895"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2025.2500895","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2025.2500895","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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/A5054778975","display_name":"Stefan Steinerberger","orcid":"https://orcid.org/0000-0002-7745-4217"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stefan Steinerberger","raw_affiliation_strings":["Department of Mathematics, University of Washington"],"raw_orcid":"https://orcid.org/0000-0002-7745-4217","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Washington","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054778975"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17624785,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"132","issue":"7","first_page":"700","last_page":"705"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9991999864578247,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9904000163078308,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6081150770187378},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.59793621301651},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4922544062137604},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3499608635902405},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09749159216880798}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6081150770187378},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.59793621301651},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4922544062137604},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3499608635902405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09749159216880798}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2025.2500895","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2025.2500895","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1505597232","https://openalex.org/W1515727144","https://openalex.org/W1982438618","https://openalex.org/W2043484420","https://openalex.org/W2063054346","https://openalex.org/W2069861310","https://openalex.org/W2077562249","https://openalex.org/W2093126960","https://openalex.org/W2100449986","https://openalex.org/W2318698654","https://openalex.org/W2811317572","https://openalex.org/W4390615451"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"We":[0,45,80],"revisit":[1],"the":[2,41,71,87],"classical":[3,48],"triangle":[4,58,76],"inequality":[5],"for":[6],"real":[7],"numbers":[8],"and":[9,60,70,86,100],"interpret":[10],"it":[11],"in":[12,37],"a":[13,51],"slightly":[14],"different":[15],"light":[16],"that":[17,55],"can":[18],"be":[19],"nicely":[20],"generalized.":[21],"This":[22],"allows":[23],"us":[24],"to":[25,40,83],"identify":[26],"general":[27],"triangle-like":[28],"inequalities":[29,59,77,85],"with":[30],"suitable":[31],"graphs.":[32],"The":[33,64],"usual":[34],"|x\u2212y|\u2264|x\u2212z|+|z\u2212y|":[35],"corresponds,":[36],"this":[38],"scheme,":[39],"graph":[42],"[insert":[43],"symbols].":[44],"show":[46],"how":[47],"ideas":[49],"give":[50,61],"characterization":[52,65],"of":[53,73,89],"graphs":[54,74],"describe":[56],"such":[57],"several":[62],"examples.":[63],"is":[66],"nice":[67],"but":[68],"nontrivial":[69],"family":[72],"describing":[75],"remains":[78],"mysterious.":[79],"discuss":[81],"connections":[82],"rearrangement":[84],"work":[88],"Larry":[90],"Harper,":[91],"Francis":[92],"Macaulay,":[93],"George":[94],"P\u00f3lya,":[95],"Alexander":[96],"Pruss,":[97],"G\u00e1bor":[98],"Szeg\u0151,":[99],"others.":[101]},"counts_by_year":[],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}