Published on:

7 April 2023

Primary Category:

Group Theory

Paper Authors:

Henry Jaspars

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Proves stable length is rational for free groups under conjugation-invariant cancellation norm

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Uses language theory to show length sequence is uniformly semi-arithmetic

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Applies to free groups and virtually free Coxeter groups

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Connects word metrics to formal language and semilinear set theory

Word length stability in free groups

This paper proves that the stable length of words in free groups, with respect to a conjugation-invariant norm equal to cancellation length, is a rational number. Through connections to formal language theory, it shows the sequence of normed lengths for powers of words is uniformly semi-arithmetic. This answers an open question about stability and rationality for certain bi-invariant metrics on groups like free groups and Coxeter groups.

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