Party-Hecke algebras

Abstract

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 transpositions. We construct a basis for this algebra and show that it can be realized as a quotient of the algebra of braids and ties. Furthermore, we study the party monoid and its relationship with the tied symmetric monoid and their associated algebras.