CANCELED: Möbius Inversion: From Number Theory to Topological Data Analysis
The classical Möbius inversion formula was introduced to number theory in 1832 by August Ferdinand Möbius. It relates two arithmetic functions (e.g., Euler’s Phi function) in terms of sums over divisors of a given integer. In 1962, Gian-Carlo Rota introduced a vast generalization of this idea for functions defined over partially ordered sets (posets). Rota applied his generalized Möbius inversion formula to numerous problems in combinatorics.