5 citations · 16 across the 11 of their papers we have counts for
12 papers
A note on the submonoids of the tied-symmetric monoid containing the symmetric group
Diego Arcis
We show that the submonoids of the tied-symmetric monoid containing the symmetric group form a distributive lattice. Furthermore, we determine a minimal generating set for any such…
On the quasisymmetric functions in superspace
Diego Arcis, Camilo González, Sebastián Márquez
Quasisymmetric functions in superspace were introduced as a natural extension of classical quasisymmetric functions involving both commuting and anticommuting variables. In this pa…
Party-Hecke algebras
Diego Arcis, Jesús Juyumaya
Party-Hecke algebras are introduced as a two-parameter deformation of party algebras, where one parameter deforms the party generators and the other deforms the elementary transpos…
On framed rook algebras
Diego Arcis, Jorge Espinoza, Marcelo Flores
We introduce and study the framed rook algebra, a structure that unifies two significant generalizations of the Iwahori-Hecke algebra. The first one, introduced by Solomon, extends…
Tied--boxed algebras
Diego Arcis, Jorge Espinoza
We introduce two new algebras that we call \emph{tied--boxed Hecke algebra} and \emph{tied--boxed Temperley--Lieb algebra}. The first one is a subalgebra of the algebra of braids a…
Symmetric functions in noncommuting variables in superspace
Diego Arcis, Camilo González, Sebastián Márquez
In 2004, Rosas and Sagan developed the theory of symmetric functions in noncommuting variables, achieving results analogous to classical symmetric functions. On the other hand, in…
Ramified inverse and planar monoids
Francesca Aicardi, Diego Arcis, Jesús Juyumaya
Ramified monoids are a class of monoids introduced by the authors. The main motivation for considering these monoids comes from knot theory, see [3, 4, 5]. Thus, in [2] we have stu…
On the Hopf algebra of noncommutative symmetric functions in superspace
Diego Arcis, Camilo González, Sebastián Márquez
We study in detail the Hopf algebra of noncommutative symmetric functions in superspace sNSym, introduced by Fishel, Lapointe and Pinto. We introduce a family of primitive elements…
Brauer and Jones tied monoids
Francesca Aicardi, Diego Arcis, Jesús Juyumaya
We introduce a ramified monoid, attached to each Brauer--type monoid, that is, to the symmetric group, to the Jones and Brauer monoids among others. Ramified monoids correspond to…
Hopf algebras on planar trees and permutations
Diego Arcis, Sebastián Márquez
We endow the space of rooted planar trees with an structure of Hopf algebra. We prove that variations of such a structure lead to Hopf algebras on the spaces of labelled trees, …
Tied Monoids
Diego Arcis, Jesús Juyumaya
We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting…
Ordering Garside groups
Diego Arcis, Luis Paris
We introduce a condition on Garside groups that we call Dehornoy structure. An iteration of such a structure leads to a left order on the group. We show conditions for a Garside gr…