标题： 带有六个四面体的超体积和两个离散曲率的公式 显示英文标题

标题： A formula with hypervolumes of six 4-simplices and two discrete curvatures

摘要： 五边形方程在高维空间中的一个推广是所谓的“六项式方程”。 从几何上讲，它对应于一种“亚历山大变换”，即单纯复形的基本重构，具体来说，就是将一个由三个4-单形组成的“簇”替换为另一个由三个4-单形组成的“簇”，并且具有相同的边界。 我们提出一个公式，其左边包含第一个簇中单形的欧几里得体积，右边包含第二个簇中单形的欧几里得体积。 该公式还涉及当我们将欧几里得空间稍作变形时出现的“离散曲率”。 显示英文摘要

摘要： One of the generalizations of the pentagon equation to higher dimensions is the so-called "six-term equation". Geometrically, it corresponds to one of the "Alexander moves", that is elementary rebuildings of simplicial complexes, namely, replacing a "cluster" of three 4-simplices by another "cluster", also of three 4-simplices and with the same boundary. We present a formula containing the euclidean volumes of the simplices in the first cluster in its l.h.s., and those in the second cluster - in its r.h.s. The formula also involves "discrete curvatures" appearing when we slightly deform the euclidean space.