AI 中文总结
本文引入序列$m$-邻接距离概念，研究其基本性质，定义单纯复形的序列$m$-离散拓扑复杂度，将拓扑复杂度经典结果扩展到单纯和$m$维情形。
AI 中文摘要
本文针对有限个单纯映射引入序列$m$-邻接距离的概念，它是邻接距离的高维类比。该不变量推广了高维邻接距离和$m$-邻接距离，为序列$m$-同伦距离提供了组合对应物。我们研究其基本性质，包括在强同伦型下的不变性、复合下的行为、范畴积以及重心重分。此外，我们定义了单纯复形的序列$m$-离散拓扑复杂度。作为应用，我们结合$m$-单纯LS范畴，通过序列$m$-邻接距离刻画该不变量，并证明它们是强同伦型的不变量。进一步，我们建立了$m$-单纯LS范畴与$m$-离散序列拓扑复杂度之间的不等式，将拓扑复杂度理论的经典结果扩展到单纯和$m$维情形。
英文摘要
In this paper, we introduce the notion of sequential $m$-contiguity distance for finitely many simplicial maps as a higher analogue of contiguity distance. This invariant generalizes both higher contiguity distance and $m$-contiguity distance, and provides a combinatorial counterpart of sequential $m$-homotopic distance. We investigate its fundamental properties, including invariance under strong homotopy type, behaviour under compositions, categorical products, and barycentric subdivision. Moreover, we define sequential $m$-discrete topological complexity of simplicial complexes. As applications, we characterise this invariant (along with $m$-simplicial LS category) in terms of sequential $m$-contiguity distance and prove that they are invariants of strong homotopy type. Furthermore, we establish inequalities relating $m$-simplicial LS category and $m$-discrete sequential topological complexity, extending classical results from topological complexity theory to the simplicial and $m$-dimensional setting.
