{"paper":{"title":"Infinite Self-Shuffling Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"\\'Emilie Charlier, Luca Q. Zamboni, Svetlana Puzynina, Teturo Kamae","submitted_at":"2013-02-15T18:42:20Z","abstract_excerpt":"In this paper we introduce and study a new property of infinite words: An infinite word $x\\in A^\\mathbb{N}$, with values in a finite set $A$, is said to be $k$-self-shuffling $(k\\geq 2)$ if $x$ admits factorizations: $x=\\prod_{i=0}^\\infty U_i^{(1)}\\cdots U_i^{(k)}=\\prod_{i=0}^\\infty U_i^{(1)}=\\cdots =\\prod_{i=0}^\\infty U_i^{(k)}$. In other words, there exists a shuffle of $k$-copies of $x$ which produces $x$. We are particularly interested in the case $k=2$, in which case we say $x$ is self-shuffling. This property of infinite words is shown to be an intrinsic property of the word and not of i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3844","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"}