Appendix C Incidence Algebras and Möbius Inversion

Abstract

The purpose of this appendix is to familiarize the reader with an important combinatorial technique that is used throughout the text. The theory of incidence algebras and Möbius inversion for posets was developed by Rota [Rot64] and can be considered as part of the origins of algebraic combinatorics. It provides a highly conceptual generalization of the principle of inclusion-exclusion. A thorough introduction, including techniques for computing the Möbius function of a poset and connections with algebraic topology, can be found in Stanley’s classic text [Sta97, Chapter 3]. Throughout this appendix, P will denote a finite poset.