AI 中文总结
本文提出与欧几里得格和沃罗诺伊胞腔几何相关的新型组合不变量晶体幽灵，证明其在各维度仅有限个存在，扩展构造至更大类组合对象，并将其用于给出完美格的沃罗诺伊有限性定理的新组合证明。
AI 中文摘要
本文引入了晶体幽灵（crystallographic wraiths），这是与欧几里得格相关联且和沃罗诺伊（Voronoï）胞腔几何相关的新型组合不变量，它们基于相关沃罗诺伊向量间最短线性依赖的几何性质。此外，本文探究晶体幽灵的新理论，证明每个维度中仅存在有限个此类对象，并将该构造扩展至更大类别的组合对象。作为应用，本文为完美格的沃罗诺伊有限性定理提供了一种新的组合证明。
英文摘要
This article introduces crystallographic wraiths, new combinatorial invariants attached to Euclidean lattices and linked to the geometry of Vorono{ï} cells. They are based on geometric properties of shortest linear dependencies among relevant Vorono{ï} vectors. Moreover, it explores the new theory of crystallographic wraiths, proves that only finitely many occur in each dimension, and extends the construction to a larger class of combinatorial objects. As an application, it provides a new combinatorial proof of Vorono{ï}'s finiteness theorem for perfect lattices.
