Yannic Vargas
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View article: Two associative operads of packed words
Two associative operads of packed words Open
The associative operad is a central structure in operad theory, defined on the linear span of the set of permutations. We build two analogs of the associative operad on the linear span of the set of packed words which turn out to be set-th…
View article: Schröder trees, antipode formulas and non-commutative probability
Schröder trees, antipode formulas and non-commutative probability Open
We obtain a cancellation-free formula, represented in terms of Schröder trees, for the antipode in the double tensor Hopf algebra introduced by Ebrahimi-Fard and Patras. We apply the antipode formula in the context of non-commutative proba…
View article: On the free commutative monoid over a positive operad
On the free commutative monoid over a positive operad Open
We study algebraic structures on the free commutative twisted algebra generated by a positive operad $\mathbf q$, in the framework of vector species. Given a nonunital commutative twisted algebra structure $μ$ on $\mathbf q$, we introduce …
View article: An operad structure on the free commutative monoid over a positive operad
An operad structure on the free commutative monoid over a positive operad Open
We study algebraic structures on the free commutative twisted algebra generated by a positive operad $\mathbf q$, in the framework of vector species. Given a nonunital commutative twisted algebra structure $\mu$ on $\mathbf q$, we introduc…
View article: Antipode formulas for pattern Hopf algebras
Antipode formulas for pattern Hopf algebras Open
The permutation pattern Hopf algebra is a commutative filtered and connected Hopf algebra. Its product structure stems from counting patterns of a permutation, interpreting the coefficients as permutation quasi-shuffles. The Hopf algebra w…
View article: Hopf algebras of parking functions and decorated planar trees
Hopf algebras of parking functions and decorated planar trees Open
We construct three new combinatorial Hopf algebras based on the Loday-Ronco operations on planar binary trees. The first and second algebras are defined on planar trees and labeled planar trees extending the Loday-Ronco and Malvenuto-Reute…
View article: Hopf algebras of parking functions and decorated planar trees
Hopf algebras of parking functions and decorated planar trees Open
We construct three new combinatorial Hopf algebras based on the Loday-Ronco operations on planar binary trees. The first and second algebras are defined on planar trees and labeled planar trees extending the Loday-Ronco and Malvenuto-Reute…