苍鹭中楣
Heronian friezes
摘要：
出于对欧几里得平面上的点配置的计算几何，并通过A型集群代数的理论，我们介绍和研究Heronian friezes，Coxeter的friezes模式的欧几里得类似物。我们证明了一个通用的Heronian frieze具有滑动对称性（因此是周期性的），并建立适当的版本的Laurent现象。对于一个密切相关的家庭凯莱门格尔friezes，我们确定了一个代数条件的连贯性，所有friezes的几何起源满足。这产生了一个明确的传播规则相干Cayley-Menger friezes，以及相应的周期性结果。
英文摘要：
Motivated by computational geometry of point configurations on the Euclidean plane, and by the theory of cluster algebras of type A, we introduce and study Heronian friezes, the Euclidean analogues of Coxeter's frieze patterns. We prove that a generic Heronian frieze possesses the glide symmetry (hence is periodic), and establish the appropriate version of the Laurent phenomenon. For a closely related family of Cayley-Menger friezes, we identify an algebraic condition of coherence, which all friezes of geometric origin satisfy. This yields an unambiguous propagation rule for coherent Cayley-Menger friezes, as well as the corresponding periodicity results.
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