Quasisymmetric functions from combinatorial Hopf monoids and Ehrhart Theory

Jacob A. White (1)

1 UTRGV - University of Texas Rio Grande Valley [Brownsville, TX]

We investigate quasisymmetric functions coming from combinatorial Hopf monoids. We show that these invariants arise naturally in Ehrhart theory, and that some of their specializations are Hilbert functions for relative simplicial complexes. This class of complexes, called forbidden composition complexes, also forms a Hopf monoid, thus demonstrating a link between Hopf algebras, Ehrhart theory, and commutative algebra. We also study various specializations of quasisymmetric functions.

Domaines: Combinatoire [math.CO]

Jacob A. White. Quasisymmetric functions from combinatorial Hopf monoids and Ehrhart Theory. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6334⟩. ⟨hal-02168182⟩