Séminaire Lotharingien de Combinatoire, 82B.91 (2019), 12 pp.
Mario Sanchez
Möbius inversion as duality for Hopf monoids
Abstract.
We study a large class of Hopf monoids which come equipped with a poset that is compatible with the Hopf structure. In these cases, we can understand duality in terms of Möbius inversion, and . We use this to give uniform proofs for cofreeness and calculations of primitives for graphs, set partitions, matroids, and scheduling problems. Moreover, we find that the Möbius function defines an important inner product for these Hopf monoids.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
The following versions are available: