105 citations · 167 across the 23 of their papers we have counts for
15 papers · 1 filter
Hopf substitutions in Species
Aaron Lauve, Anthony Lazzeroni
In the theory of species, the species of linear orders and the substitution operation combine for a compelling result: given any positive comonoid…
Interpolation in Species and a Lift of the Hopf Algebra of r-Quasisymmetric Functions
Aaron Lauve, Anthony Lazzeroni
In this manuscript we lift the theory of r-quasisymmetric functions to the theory of Hopf monoids. We provide a general method of interpolating between two Hopf monoids, one being…
Rational series in the free group and the Connes operator
Aaron Lauve, Christophe Reutenauer
We characterize rational series over the free group by using an operator introduced by A. Connes. We prove that rational Malcev--Neumann series posses rational expressions without…
Skew Pieri Rules for Hall-Littlewood Functions
Matjaz Konvalinka, Aaron Lauve
We produce skew Pieri Rules for Hall--Littlewood functions in the spirit of Assaf and McNamara. The first two were conjectured by the first author. The key ingredients in the proof…
Lagrange's Theorem for Hopf Monoids in Species
Marcelo Aguiar, Aaron Lauve
Following Radford's proof of Lagrange's theorem for pointed Hopf algebras, we prove Lagrange's theorem for Hopf monoids in the category of connected species. As a corollary, we obt…
Cofree compositions of coalgebras (extended abstract)
Stefan Forcey, Aaron Lauve, Frank Sottile
We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and the theory of species. We prove that the composition of two cofree…