{"paper":{"title":"Shuffling matrices, Kronecker product and Discrete Fourier Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alfredo Donno, Daniele D'Angeli","submitted_at":"2016-05-31T13:58:07Z","abstract_excerpt":"We define and investigate a family of permutations matrices, called shuffling matrices, acting on a set of $N=n_1\\cdots n_m$ elements, where $m\\geq 2$ and $n_i\\geq 2$ for any $i=1,\\ldots, m$. These elements are identified with the vertices of the $m$-th level of a rooted tree with branch indices $(n_1,\\ldots, n_m)$. Each of such matrices is induced by a permutation of $Sym(m)$ and it turns out that, in the case in which one considers the cyclic permutation $(1\\ \\ldots\\ m)$, the corresponding permutation is the classical perfect shuffle. We give a combinatorial interpretation of these permutati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09635","kind":"arxiv","version":1},"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"}