This paper presents a discrete analog of topological complexity for finite spaces using purely combinatorial terms. We demonstrate that this coincides with the genuine topological complexity of the original finite space. Furthermore, we study the relationship with simplicial complexity for simplicial complexes by taking the barycentric subdivision into account.
"A combinatorial description of topological complexity for finite spaces." Algebr. Geom. Topol. 18 (2) 779 - 796, 2018. https://doi.org/10.2140/agt.2018.18.779