In this paper, we define a new flavour of well-composedness, called strong Euler well-composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an \((n-1)\)-dimensional ball. Working in the particular setting of cubical complexes canonically associated with \(n\)D pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension \(n\ge 2\) and that the converse is not true when \(n\ge 4\).

中文翻译：

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强欧拉良好组合性

在本文中，我们定义了一种新的结构良好的风格，称为强欧拉结构良好。在规则单元复合体的一般设置中，如果每个边界单元的链接的欧拉特征为1，则一个n维的规则单元复合体是强欧拉合合的，这是\((n-1) \) -维球。在与\(n\) D 图片规范相关的立方复合体的特定设置中工作，我们在本文中正式证明，强欧拉良好构图意味着任何维度\(n\ge 2\) 的数字构图良好，并且当\(n\ge 4\)时，则相反。