5 citations · 16 across the 11 of their papers we have counts for
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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…
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…
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…
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…