{"paper":{"title":"Rahman polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Ryu Sasaki","submitted_at":"2023-10-27T02:10:42Z","abstract_excerpt":"Two very closely related Rahman polynomials are constructed explicitly as the left eigenvectors of certain multi-dimensional discrete time Markov chain operators $K_n^{(i)}({\\boldsymbol x},{\\boldsymbol y};N)$, $i=1,2$. They are convolutions of an $n+1$-nomial distribution $W_n({\\boldsymbol x};N)$ and an $n$-tuple of binomial distributions $\\prod_{i}W_1(x_i;N)$. The one for the original Rahman polynomials is $K_n^{(1)}({\\boldsymbol x},{\\boldsymbol y};N) =\\sum_{\\boldsymbol z}W_n({\\boldsymbol x}-{\\boldsymbol z};N-\\sum_{i}z_i) \\prod_{i}W_1(z_i;y_i)$. The closely related one is \\ $K_n^{(2)}({\\bolds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.17853","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.17853/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}