133 citations · 518 across the 31 of their papers we have counts for
31 papers
Configuration spaces and peak representations
Marcelo Aguiar, Sarah Brauner, Victor Reiner
Within the group algebras of the symmetric and hyperoctahedral groups, one has their descent algebras and families of Eulerian idempotents. These idempotents are known to generate…
Associahedra, cyclohedra and inversion of power series
Marcelo Aguiar, Jose Bastidas
We introduce the Hopf monoid of sets of cycles and paths, which contains the Faà di Bruno Hopf monoid as a submonoid. We give cancellation-free and grouping-free formulas for its a…
Dendriform Algebras Relative to a Semigroup
Marcelo Aguiar
Loday's dendriform algebras and its siblings pre-Lie and zinbiel have received attention over the past two decades. In recent literature, there has been interest in a generalizatio…
Characteristic elements for real hyperplane arrangements
Marcelo Aguiar, Jose Bastidas, Swapneel Mahajan
Characteristic elements of the Tits algebra of a real hyperplane arrangement carry information about the characteristic polynomial. We present this notion and its basic properties,…
Hopf monoids and generalized permutahedra
Marcelo Aguiar, Federico Ardila
Generalized permutahedra are a family of polytopes with a rich combinatorial structure and strong connections to optimization. We prove that they are the universal family of polyhe…
Monads on higher monoidal categories
Marcelo Aguiar, Mariana Haim, Ignacio Lopez Franco
We study the action of monads on categories equipped with several monoidal structures. We identify the structure and conditions that guarantee that the higher monoidal structure is…