{"paper":{"title":"Combinatorial aspects of orthogonal group integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Jean-Marc Schlenker, Teodor Banica","submitted_at":"2010-11-10T18:37:31Z","abstract_excerpt":"We study the integrals of type $I(a)=\\int_{O_n}\\prod u_{ij}^{a_{ij}}\\,du$, depending on a matrix $a\\in M_{p\\times q}(\\mathbb N)$, whose exact computation is an open problem. Our results are as follows: (1) an extension of the \"elementary expansion\" formula from the case $a\\in M_{2\\times q}(2\\mathbb N)$ to the general case $a\\in M_{p\\times q}(\\mathbb N)$, (2) the construction of the \"best algebraic normalization\" of $I(a)$, in the case $a\\in M_{2\\times q}(\\mathbb N)$, (3) an explicit formula for $I(a)$, for diagonal matrices $a\\in M_{3\\times 3}(\\mathbb N)$, (4) a modelling result in the case $a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2454","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}