{"id":"https://openalex.org/W7212224344","doi":"https://doi.org/10.48550/arxiv.2609.11774","title":"Circular Rearrangement Inequality and Optimal Cyclic Birth and Death Chains","display_name":"Circular Rearrangement Inequality and Optimal Cyclic Birth and Death Chains","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212224344","doi":"https://doi.org/10.48550/arxiv.2609.11774"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.11774","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11774","pdf_url":"https://arxiv.org/pdf/2609.11774","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.11774","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024684015","display_name":"Gabriel Raposo","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Raposo, Gabriel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5024684015"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.5576000213623047,"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"}},"topics":[{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.5576000213623047,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.33640000224113464,"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/T13500","display_name":"Probability and Statistical Research","score":0.066600002348423,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/birth-death-processes","display_name":"birth-death processes","score":0.6579999923706055}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8036999702453613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7419000267982483},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6376000046730042},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.48500001430511475},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.46810001134872437},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29829999804496765},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.2851000130176544},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.11774","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11774","pdf_url":"https://arxiv.org/pdf/2609.11774","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.11774","doi":"https://doi.org/10.48550/arxiv.2609.11774","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.11774","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.11774","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11774","pdf_url":"https://arxiv.org/pdf/2609.11774","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212224344.pdf","grobid_xml":"https://content.openalex.org/works/W7212224344.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1575337302","https://openalex.org/W3044992816"],"related_works":["https://openalex.org/W7214214767","https://openalex.org/W2892507974","https://openalex.org/W1673274929","https://openalex.org/W7098424264","https://openalex.org/W25289240","https://openalex.org/W2078755195","https://openalex.org/W3008959764","https://openalex.org/W2041636323","https://openalex.org/W2044839118","https://openalex.org/W7162942755"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2,12,36,66],"generalized":[3],"circular":[4,9,45],"rearrangement":[5,46],"inequality:":[6],"among":[7],"all":[8],"arrangements":[10],"of":[11,15,25,27,39,50,65,73],"finite":[13],"collection":[14],"positive":[16],"numbers,":[17],"the":[18,23,43,59,63,74],"greedy":[19,60],"arrangement":[20],"simultaneously":[21],"maximizes":[22],"sums":[24],"products":[26,49],"$k$":[28],"consecutive":[29],"entries":[30],"for":[31,48],"every":[32],"$k$.":[33],"This":[34],"resolves":[35],"2023":[37],"conjecture":[38,72],"Holmes-Holroyd-Ram\u00edrez":[40],"and":[41],"extends":[42],"classical":[44],"inequality":[47],"adjacent":[51],"entries.":[52],"As":[53],"an":[54],"application,":[55],"we":[56],"show":[57],"that":[58],"ordering":[61],"minimizes":[62],"speed":[64],"cyclic":[67],"birth-and-death":[68],"chain,":[69],"resolving":[70],"another":[71],"same":[75],"authors.":[76]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-12T00:00:00"}
