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- W2968228214 abstract "In this paper we introduce and study a new property of infinite words which is invariant under the action of a morphism: We say an infinite word $xin A^nats,$ defined over a finite alphabet $A,$ is self-shuffling if $x$ admits factorizations: $x=prod_{i=1}^infty U_iV_i=prod_{i=1}^infty U_i=prod_{i=1}^infty V_i$ with $U_i,V_i in A^+.$ In other words, there exists a shuffle of $x$ with itself which reproduces $x.$ The morphic image of any self-shuffling word is again self-shuffling. We prove that many important and well studied words are self-shuffling: This includes the Thue-Morse word and all Sturmian words (except those of the form $aC$ where $ain {0,1}$ and $C$ is a characteristic Sturmian word). We further establish a number of necessary conditions for a word to be self-shuffling, and show that certain other important words (including the paper-folding word and infinite Lyndon words) are not self-shuffling. In addition to its morphic invariance, which can be used to show that one word is not the morphic image of another, this new notion has other unexpected applications: For instance, as a consequence of our characterization of self-shuffling Sturmian words, we recover a number theoretic result, originally due to Yasutomi, which characterizes pure morphic Sturmian words in the orbit of the characteristic." @default.
- W2968228214 created "2019-08-22" @default.
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- W2968228214 date "2013-02-15" @default.
- W2968228214 modified "2023-09-26" @default.
- W2968228214 title "Self-Shuffling Words" @default.
- W2968228214 hasPublicationYear "2013" @default.
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