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arXiv · 2605.15027

Chains of affine standard Lyndon words

Corbet Elkins·Alexander Tsymbaliuk
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Abstract

In this note, we establish the periodicity of chains of affine standard Lyndon words in all types and determine tight bounds on that periodicity, greatly generalizing the $A$-type results of arXiv:2305.16299. Our approach crucially utilizes the convexity and monotonicity of arXiv:2505.15432 together with the new idea to consider the polarization of the root system given by increasing and decreasing chains.

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Corbet Elkins, Alexander Tsymbaliuk. 2026-05-14. Chains of affine standard Lyndon words. https://arxiv.org/abs/2605.15027

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