标题： 一些行列式和关系在海伦数表中 显示英文标题

标题： Some determinants and relations in Heronian friezes

摘要： 本文中，我们给出了单个由循环$n$多边形产生的Heronian行列式中元素所满足的代数关系和行列式消失恒等式。 我们也给出了此类Heronian行列式中多个相邻diamonds之间元素所满足的代数关系。 此外，我们定义了一个平面Heronian行列式，并建立了由循环$n$多边形产生的平面Heronian行列式中元素的一些更多的行列式消失恒等式，其中$n$是一个正整数且能被$4$整除。 显示英文摘要

摘要： In this article, we give algebraic relations and determinant vanishing equalities that hold for the entries of a single Heronian diamond of a Heronian frieze arising from a cyclic $n$-gon. We also give algebraic relations that hold between entries of multiple adjacent diamonds of such a frieze. Furthermore, we define a plane Heronian frieze, and establish some more determinant vanishing equalities for the entries of a plane Heronian frieze arising from a cyclic $n$-gon, where $n$ is a positive integer divisible by $4$.