{"id":"https://openalex.org/W7216290390","doi":"https://doi.org/10.48550/arxiv.2610.00599","title":"A Combinatorial Approach to the CUE Joint Moment Problem","display_name":"A Combinatorial Approach to the CUE Joint Moment Problem","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7216290390","doi":"https://doi.org/10.48550/arxiv.2610.00599"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.00599","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00599","pdf_url":"https://arxiv.org/pdf/2610.00599","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/2610.00599","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5155097722","display_name":"George Snape","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Snape, George","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5155097722"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T11716","display_name":"Random Matrices and Applications","score":0.6532999873161316,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.6532999873161316,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.22390000522136688,"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/T11166","display_name":"Analytic Number Theory Research","score":0.039400000125169754,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/circular-unitary-ensemble","display_name":"circular unitary ensemble","score":0.828000009059906},{"id":"https://openalex.org/keywords/joint-moments","display_name":"joint moments","score":0.925000011920929},{"id":"https://openalex.org/keywords/unit-circle","display_name":"unit circle","score":0.718999981880188},{"id":"https://openalex.org/keywords/even-exponents","display_name":"even exponents","score":0.7049999833106995},{"id":"https://openalex.org/keywords/asymptotic-behavior","display_name":"asymptotic behavior","score":0.5910000205039978},{"id":"https://openalex.org/keywords/kostka-numbers","display_name":"Kostka numbers","score":0.9869999885559082},{"id":"https://openalex.org/keywords/magic-squares","display_name":"magic squares","score":0.8939999938011169},{"id":"https://openalex.org/keywords/integer-matrices","display_name":"integer matrices","score":0.7799999713897705},{"id":"https://openalex.org/keywords/conformal-blocks","display_name":"conformal blocks","score":0.7360000014305115},{"id":"https://openalex.org/keywords/random-matrix-theory","display_name":"random matrix theory","score":0.6539999842643738}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.728600025177002},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6891999840736389},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6158000230789185},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6018999814987183},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5712000131607056},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48159998655319214},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.4749999940395355},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4607999920845032},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C4285052","wikidata":"https://www.wikidata.org/wiki/Q3406268","display_name":"Moment problem","level":3,"score":0.3343000113964081},{"id":"https://openalex.org/C2779521423","wikidata":"https://www.wikidata.org/wiki/Q3855646","display_name":"Combinatorial method","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2621000111103058},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.25049999356269836},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.00599","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00599","pdf_url":"https://arxiv.org/pdf/2610.00599","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.2610.00599","doi":"https://doi.org/10.48550/arxiv.2610.00599","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.00599","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:2610.00599","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00599","pdf_url":"https://arxiv.org/pdf/2610.00599","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/W7216290390.pdf","grobid_xml":"https://content.openalex.org/works/W7216290390.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1638043019","https://openalex.org/W2004238784","https://openalex.org/W2037236081","https://openalex.org/W2064107124","https://openalex.org/W2101367141","https://openalex.org/W2167300917","https://openalex.org/W2899212530","https://openalex.org/W3084239242","https://openalex.org/W4394011465","https://openalex.org/W4400089371","https://openalex.org/W4406772036","https://openalex.org/W7128922611","https://openalex.org/W7138879563","https://openalex.org/W7151058686"],"related_works":["https://openalex.org/W3131366646","https://openalex.org/W2152116619","https://openalex.org/W2162688851","https://openalex.org/W2962981400","https://openalex.org/W7106690518","https://openalex.org/W2374343410","https://openalex.org/W1836203413","https://openalex.org/W2122700529","https://openalex.org/W2948216389","https://openalex.org/W2074572283"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,63,75],"give":[4],"exact":[5],"combinatorial":[6],"expressions":[7,35],"for":[8,36],"all":[9,21],"CUE":[10],"joint":[11],"moments":[12],"on":[13],"the":[14,18,28,39,47,68],"unit":[15],"circle,":[16],"in":[17,67],"case":[19],"that":[20],"exponents":[22],"are":[23],"even":[24],"positive":[25],"integers,":[26],"yielding":[27],"corresponding":[29],"asymptotics.":[30],"We":[31],"offer":[32],"two":[33],"equivalent":[34],"these":[37],"quantities:":[38],"first":[40],"is":[41,49],"a":[42,77],"sum":[43],"involving":[44],"Kostka":[45],"numbers;":[46],"second":[48],"related":[50],"to":[51],"counting":[52],"integer":[53],"matrices":[54],"(magic":[55],"squares).":[56],"As":[57],"an":[58,85],"application":[59],"of":[60,79],"our":[61],"results,":[62],"unify":[64],"many":[65],"results":[66],"literature,":[69],"which":[70],"were":[71],"previously":[72],"disconnected.":[73],"Moreover,":[74],"prove":[76],"conjecture":[78],"Basor":[80],"et":[81],"al.":[82],"(2018)":[83],"regarding":[84],"irregular":[86],"conformal":[87],"block":[88],"structure.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}