Resumen de Covering-based numbers related to the LS-category of finite spaces

Manuel Cárdenas, Ramón Flores, Antonio Rafael Quintero Toscano , María Trinidad Villar Liñán

• In this paper, we consider the Lusternik–Schnirelmann and geometric categories of finite spaces. We define new numerical invariants for these spaces derived from the geometric category and present an algorithmic approach for their effective computation. Our analysis combines homotopy-theoretic properties of these spaces with algorithms and tools from graph and hypergraph theory. We also provide several examples to illustrate our results.