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math.RT2026
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…
math.RT2026
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…
math.RT2025
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…