Mixing properties for some classes of permutations on f£

In the class F_n,_k of permutations on F^ with coordinate functions essentially depending on exactly k variables, k < n, we consider two subclasses S_n,_k and P_n,_k. The method for constructing a function F(x₁,..., x_n) = (f-]_,..., f_n) G G S_n,_k starts from some function G(x₁,...,x_k) = (g₁,...,g_k) G F_k,_k. Then we set fi(x1,... ,xn) = gi(x1,... ,xk) for i = 1,... ,k and fi(x_b ... ,xn) = xi 0 hi(x_b ... ,xi-1) for i = k + 1,... ,n, where h_i is any function essentially depending on exactly k - 1 variables from ... ,x_i-1. The method for constructing a function F G P_n,_k is used in the case when k|n, i.e. n = sk for some s G N. We construct s functions G₁,... ,G_s G F_k,_k, Gi = ^1ⁱ⁾ ,...,g^<k⁾^j , i = 1,...,s, and set ftk+i(x1,... ,x,_n) = gf⁺¹⁾(x_tk+1,... ,x (t+1)k), t = 0,...,s - 1, i = 1,... ,k. Mixing properties of such function are discussed, an algorithm for calculating elementary exponents is given.

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