{"id":"https://openalex.org/W7213393228","doi":"https://doi.org/10.48550/arxiv.2609.16264","title":"On symmetric partition lattices and probability interactions","display_name":"On symmetric partition lattices and probability interactions","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213393228","doi":"https://doi.org/10.48550/arxiv.2609.16264"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.16264","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16264","pdf_url":"https://arxiv.org/pdf/2609.16264","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/2609.16264","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057266322","display_name":"Jean Carlo Guella","orcid":"https://orcid.org/0000-0001-6130-5455","observed_orcids":["https://orcid.org/0000-0001-6130-5455"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Guella, Jean Carlo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5057266322"],"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.6704000234603882,"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":0.6704000234603882,"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":0.3019999861717224,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.004100000020116568,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mobius-function","display_name":"M\u00f6bius function","score":0.9520000219345093},{"id":"https://openalex.org/keywords/permutation-invariance","display_name":"permutation invariance","score":0.8399999737739563},{"id":"https://openalex.org/keywords/integer-partitions","display_name":"integer partitions","score":0.968999981880188},{"id":"https://openalex.org/keywords/characteristic-function","display_name":"characteristic function","score":0.9700000286102295},{"id":"https://openalex.org/keywords/bernstein-functions","display_name":"Bernstein functions","score":0.9070000052452087}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7983999848365784},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5730999708175659},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5360000133514404},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4779999852180481},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4693000018596649},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.45890000462532043},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.44929999113082886},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4440000057220459},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4189999997615814},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3725999891757965},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.33959999680519104},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32010000944137573},{"id":"https://openalex.org/C72396439","wikidata":"https://www.wikidata.org/wiki/Q16000505","display_name":"Symmetric probability distribution","level":3,"score":0.29829999804496765},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.26420000195503235}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.16264","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16264","pdf_url":"https://arxiv.org/pdf/2609.16264","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.2609.16264","doi":"https://doi.org/10.48550/arxiv.2609.16264","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.16264","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:2609.16264","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16264","pdf_url":"https://arxiv.org/pdf/2609.16264","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213393228.pdf","grobid_xml":"https://content.openalex.org/works/W7213393228.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2039551466","https://openalex.org/W2144232853","https://openalex.org/W2088986669","https://openalex.org/W2082593445","https://openalex.org/W935856864","https://openalex.org/W2949108772","https://openalex.org/W2108822671","https://openalex.org/W132752629","https://openalex.org/W179979639","https://openalex.org/W2050851974"],"abstract_inverted_index":{"The":[0],"M\u00f6bius":[1,47,142],"function":[2],"of":[3,13,31,68,75,117,153],"a":[4,18,21,43,93,118,172,183],"partition":[5,23,58,120,138,174],"lattice":[6,24,121],"can":[7],"be":[8],"used":[9],"to":[10,73,100,125,171],"define":[11,114,133],"interactions":[12],"probability":[14,55,104],"measures.":[15],"We":[16,34,87,113,128,180],"call":[17],"lower":[19,78,94,178],"set":[20,95],"symmetric":[22,119],"when":[25,166],"it":[26,124],"is":[27,71],"invariant":[28],"under":[29],"permutations":[30],"the":[32,50,81,90,115,134,167,176],"variables.":[33],"characterize":[35,89],"these":[36],"lattices":[37],"through":[38],"integer":[39],"partitions":[40,91],"and":[41,106,122,132,136],"obtain":[42],"recursion":[44],"for":[45,102,144,186],"their":[46],"coefficients":[48,143],"at":[49],"top":[51],"element.":[52],"By":[53],"constructing":[54],"measures":[56],"whose":[57],"products":[59],"are":[60,84],"linearly":[61],"independent,":[62],"we":[63,147,159],"show":[64,160],"that":[65,74,96,161],"permutation":[66],"invariance":[67],"an":[69,98,162],"interaction":[70,99,149,163],"equivalent":[72],"its":[76],"underlying":[77,177],"set,":[79],"provided":[80],"coordinate":[82],"spaces":[83],"sufficiently":[85],"large.":[86],"also":[88,181],"on":[92],"force":[97],"vanish":[101],"every":[103],"measure,":[105],"construct":[107],"indecomposable":[108],"distributions":[109],"with":[110],"zero":[111],"interaction.":[112],"order":[116],"relate":[123],"vanishing":[126],"marginals.":[127],"study":[129],"generalized":[130],"Lancaster":[131],"Streitberg":[135],"size-limited":[137],"lattices,":[139],"obtaining":[140],"explicit":[141],"them.":[145],"Finally,":[146],"express":[148],"equations":[150],"in":[151,175],"terms":[152],"characteristic":[154,188],"functions.":[155,193],"For":[156],"Gaussian":[157],"distributions,":[158],"vanishes":[164],"exactly":[165],"distribution":[168],"factorizes":[169],"according":[170],"nontrivial":[173],"set.":[179],"give":[182],"nonvanishing":[184],"criterion":[185],"radial":[187],"functions":[189],"generated":[190],"by":[191],"Bernstein":[192]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-17T00:00:00"}
