Möbius Inversion and Persistence in Algebraic Topology

Learn about the mathematical relationship between Möbius inversion and persistence in this 10-minute tutorial from the Applied Algebraic Topology Network. Explore how to compute the Möbius inverse (combinatorial derivative) of a real-valued function on a locally finite poset, and discover the deep connection between algebraic combinatorics and persistence theory. Understand how the persistence diagram represents the Möbius inverse of the rank function and see how this concept extends to multiparameter persistence applications.