Conjugate Words
We define a pair of words in A∗ of the form uv and vu as conjugate: the conjugates of a word are thus its circular shifts. Two words are conjugate in this sense if they are conjugate in the sense of group theory as elements of the free group generated by A.
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“It was only just words, words,—they meant nothing in the world to him, I might just as well have whistled. Words realize nothing, vivify nothing to you, unless you have suffered in your own person the thing which the words try to describe.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)