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arXiv · 1611.01061

A Self-Referential Property of Zimin Words

John Connor
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Abstract

This paper gives a short overview of Zimin words, and proves an interesting property of their distribution. Let $L_q^m$ to be the lexically ordered sequence of $q$-ary words of length $m$, and let $T_n(L_q^m)$ to be the binary sequence where the $i$-th term is $1$ if and only if the $i$-th word of $L_q^m$ encounters the $n$-th Zimin word, $Z_n$. We show that the sequence $T_n(L_q^m)$ is an instance of $Z_{n+1}$ when $1 < n$ and $m=2^n-1$.

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John Connor. 2016-11-03. A Self-Referential Property of Zimin Words. https://arxiv.org/abs/1611.01061

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