无限中楣的簇代数解释
Cluster algebraic interpretation of infinite friezes
摘要：
最初由康威和考克斯特研究，中楣出现在各种娱乐数学出版物在20世纪70年代。最近，在2015年，鲍尔、帕森斯和查博尔德构造了周期性的无限中楣，并将它们与曾经被刺穿的圆盘和环中的匹配数字联系起来。在本文中，我们研究这样的无限friezes与眼睛对集群代数的D型和仿射A，分别。通过研究无限friezes与洛朗多项式条目，我们发现新的对称性和公式有关的条目，这个friezes到另一个。最后，我们还提出了一个对应Broline，Crowe和Isaacs的经典匹配元组和组合解释的元素从曲面的集群代数。
英文摘要：
Originally studied by Conway and Coxeter, friezes appeared in various recreational mathematics publications in the 1970s. More recently, in 2015, Baur, Parsons, and Tschabold constructed periodic infinite friezes and related them to matching numbers in the once-punctured disk and annulus. In this paper, we study such infinite friezes with an eye towards cluster algebras of type D and affine A, respectively. By examining infinite friezes with Laurent polynomial entries, we discover new symmetries and formulas relating the entries of this frieze to one another. Lastly, we also present a correspondence between Broline, Crowe and Isaacs's classical matching tuples and combinatorial interpretations of elements of cluster algebras from surfaces.
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