Analysis of affine standard lyndon words shows generalization of convexity in types, suggesting new structures.
In this note, we establish the convexity and monotonicity for affine standard Lyndon words in all types, generalizing the A-type results of arXiv:2305.16299. We also derive partial results on the structure of imaginary standard Lyndon words and present a conjecture for their general form. Additionally, we provide computer code in Appendix which, in particular, allows to efficiently compute affine standard Lyndon words in exceptional types for all orders.
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Elkins et al. (2025) studied this question.
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