Temperley–Lieb algebra approach to Catalan states of generalized crossing and lattice crossing

Abstract

Using algebraic approach, we show which elements of a basis (in the reduced form) of Temperley–Lieb algebra can be obtained as Kauffman states of lattice crossing and generalized crossing. In addition, we give an algorithm for finding them and we obtain further results concerning coefficients of the Catalan states that can be obtained as Kauffman states of [Formula: see text] lattice crossing.