Affine standard Lyndon words
arXiv:2505.15432
Abstract
In this note, we establish the convexity and monotonicity for affine standard Lyndon words in all types, generalizing the -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.
v1: 45 pages, comments are welcome!