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• W2949553407 abstract "We regard a finite word $u=u_1u_2cdots u_n$ up to word isomorphism as an equivalence relation on ${1,2,ldots, n}$ where $i$ is equivalent to $j$ if and only if $x_i=x_j.$ Some finite words (in particular all binary words) are generated by {it palindromic} relations of the form $ksim j+i-k$ for some choice of $1leq ileq jleq n$ and $kin {i,i+1,ldots,j}.$ That is to say, some finite words $u$ are uniquely determined up to word isomorphism by the position and length of some of its palindromic factors. In this paper we study the function $mu(u)$ defined as the least number of palindromic relations required to generate $u.$ We show that every aperiodic infinite word must contain a factor $u$ with $mu(u)geq 3,$ and that some infinite words $x$ have the property that $mu(u)leq 3$ for each factor $u$ of $x.$ We obtain a complete classification of such words on a binary alphabet (which includes the well known class of Sturmian words). In contrast for the Thue-Morse word, we show that the function $mu$ is unbounded." @default.
• W2949553407 created "2019-06-27" @default.
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• W2949553407 date "2015-01-01" @default.
• W2949553407 modified "2023-10-18" @default.
• W2949553407 title "On Generating Binary Words Palindromically" @default.
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