ABSTRACTLet Sn denote the symmetric group on {1,2,…,n}. For two permutations u,v∈Sn with u≤v in the Bruhat order, let Ru,v(q) and be the Kazhdan-Lusztig R-polynomial and -polynomial indexed by u and v, respectively. For 1≤i<j≤n, denote (i,j) by the transposition that interchanges the elements i and j. Let p be a permutation on {1,2,3,4}. By a p-nesting -polynomial, we mean an -polynomial , where such that and the subsequence of u is order-isomorphic to p. When p = 1324, Pagliacci found an explicit formula for 1324-nesting -polynomials. In this paper, we aim to compute p-nesting -polynomials for p = 1234.