Chains of affine standard Lyndon words
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909043977617408 |
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| author | Elkins, Corbet Tsymbaliuk, Alexander |
| author_facet | Elkins, Corbet Tsymbaliuk, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15027 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chains of affine standard Lyndon words Elkins, Corbet Tsymbaliuk, Alexander Representation Theory Combinatorics Quantum Algebra 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. |
| title | Chains of affine standard Lyndon words |
| topic | Representation Theory Combinatorics Quantum Algebra |
| url | https://arxiv.org/abs/2605.15027 |