تقرير
Y-frieze patterns
| العنوان: | Y-frieze patterns |
|---|---|
| المؤلفون: | Germain, Antoine de Saint |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Commutative Algebra, Mathematics - Rings and Algebras, 13F60 |
| الوصف: | Motivated by cluster ensembles, we introduce a new variant of frieze patterns associated to acyclic cluster algebras, which we call ${\bf Y}\textit{-frieze patterns}$. Using the mutation rules for ${\bf Y}$-variables, we define a large class of ${\bf Y}$-frieze patterns called $\textit{unitary }{\bf Y}\textit{-frieze patterns}$, and show that the ensemble map induces a map from (unitary) frieze patterns to (unitary) ${\bf Y}$-frieze patterns. In rank 2, we show that ${\bf Y}$-frieze patterns are (associated to) friezes of generalised cluster algebras. In finite type (not necessarily rank 2), we show that ${\bf Y}$-frieze patterns share the same symmetries as frieze patterns, and prove that their number is finite. Comment: Some notation changed, Section 4 on the case of rank 2 added. The finiteness conjecture of v1 is now Theorem 5.5 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.03073 |
| رقم الأكسشن: | edsarx.2311.03073 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |